{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 22\n",
    "\n",
    "# 统计 + 线性代数\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfa980bb-6ce2-4396-a4ce-bc6af5637d1f",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "这段代码对鸢尾花数据集进行分析和可视化，目的是探索数据特征的中心化、协方差矩阵和相关矩阵的分布特性。首先，代码从Seaborn和Scikit-Learn中加载鸢尾花数据，并将特征矩阵 $X$ 转换为DataFrame格式，便于进一步操作。代码生成了原始特征矩阵 $X$ 的热力图，展示每个特征的数值范围。\n",
    "\n",
    "随后，代码计算了 $X$ 的质心（均值向量） $E_X = \\frac{1}{N} \\sum_{i=1}^N X_i$ ，并生成去均值后的数据矩阵 $X_{demean} = X - E_X$，使数据围绕原点对称分布。对于去均值矩阵，代码绘制了其热力图和各列特征的核密度估计图，以观察去均值后特征的分布形态。\n",
    "\n",
    "代码还计算了特征矩阵 $X$ 的协方差矩阵 $\\Sigma = \\frac{1}{N} X_{demean}^T X_{demean}$ 和相关矩阵 $\\rho$，并分别绘制它们的热力图来展示特征间的协方差和相关性。\n",
    "\n",
    "最后，代码按类别（Setosa、Versicolor、Virginica）分别计算并绘制每一类数据的协方差矩阵和相关矩阵，以比较不同类别中各特征之间的协方差和相关性差异。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c7fdffd3-b15a-4ac6-9d06-1d7d03908e32",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入 numpy 进行数值计算\n",
    "import matplotlib.pyplot as plt  # 导入 matplotlib 用于绘图\n",
    "import pandas as pd  # 导入 pandas 进行数据操作\n",
    "import seaborn as sns  # 导入 seaborn 进行数据可视化\n",
    "from sklearn.datasets import load_iris  # 从 sklearn 加载鸢尾花数据集"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87155e44-3825-4aa6-897c-04d4f5a49fa8",
   "metadata": {},
   "source": [
    "## 加载鸢尾花数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8f1517a8-1341-47a1-b5fd-35c03da9b112",
   "metadata": {},
   "outputs": [],
   "source": [
    "iris_sns = sns.load_dataset(\"iris\")  # 从 seaborn 加载鸢尾花数据集副本\n",
    "iris = load_iris()  # 从 sklearn 加载鸢尾花数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b7765e8f-261c-49d4-b8b7-14c8072359fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris.data  # 特征矩阵 X\n",
    "y = iris.target  # 目标标签 y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "77cf6ba5-d114-454b-9620-b1009da4da4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_names = ['Sepal length, x1','Sepal width, x2',\n",
    "                 'Petal length, x3','Petal width, x4']  # 特征名称"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00805382-4ded-464c-815b-b935c9a7f319",
   "metadata": {},
   "source": [
    "## 将特征矩阵 X 转换为 DataFrame 格式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fae93351-9d65-4916-92f6-9a5e2b5fffb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_df = pd.DataFrame(X, columns=feature_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6f9b2b3-3b2f-4794-aaa5-32b44f77f022",
   "metadata": {},
   "source": [
    "## 可视化特征矩阵的热力图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9e1a7e08-d8cc-492f-8d87-2fd55fe6ebaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_style(\"ticks\")  # 设置 seaborn 绘图风格"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7615de77-e451-43c1-9aef-f4bbcee60b0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X_df.to_numpy()  # 转换 DataFrame 为 numpy 数组"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ce250ce0-5239-4bba-a166-c5477da7319e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'X')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UFPDzuzFhkR7TosSyvMrq+ImIiIyIyX/H//vvv+N///sfrl69CltbW7zyyisIDQ2FjY0Nzp49i/DwcCQmJsLR0RETJkxAQECAmM2ThAoEa7kjUBF1fp7cEYhIQUSbo0hLS0NQUBCGDRuGEydOYNeuXTh27Bg+++wzZGZmYty4cejfvz+OHz+OiIgILFq0COfOnROreSIiIsmZmatEuUlJtBF/rVq18Ntvv8He3h6CICAjIwOPHj1CrVq18MMPP8DBwQHDhw8HAHTp0gV+fn6IjY1F27ZtxYpAREQkKZOf6re3twcAdO/eHffu3YOHhwcGDhyI5cuXw9XVVedYFxcX7Nixo3wN1HEWKypVkrqQlROMhZ1todwRiEwWL+cr8sMPP+DQoUMwMzNDSEgIsrOzYWtrq3OMjY0NcnJyqqJ5IiIiKkOVrOq3sbGBjY0NQkNDERAQgJEjR+Lhw4c6x+Tl5T2xRK/e6nwFvEzGWHBxHxGRMqf6RRvxnzp1Cq+88opOZ61Wq2FpaQkXFxdcuXJF5/jExEQ0b968zPNFR0fD3d1d50ZERGRUzFXi3CQkWsffokUL5OXlYenSpVCr1bhz5w6WLFkCf39/+Pr64v79+9i4cSPy8/Nx5MgRfPPNNxg0aFCZ5wsKCsLJkyd1bkRERFQ5ok31V6tWDTExMVi4cCG6du2K6tWrw8/PD8HBwbCyssL69esRERGByMhI1KpVC3PmzEHnzp3LPJ/e6nyX74gVlyrJrlaa3BGoSEGBRu4IVAKL9JgWJU71i/odv4uLC9avX6/3sTZt2mDbtm1iNkdERCQvc27ZW7XsbJ9+DEmitsUluSOQVjO5A1AJDzO4kyIZN2V1/ERERMbE1Kf6iYiITIkSN/BRVMcvZGbKHYGKqAry5Y5ARdT53LnPmJhbKu87XzItiur4iYiIjIqpT/U/qSzvpUuXtBX5bG1t4efnh9DQUFhYGB5B1bCRmHGpEm4VdJc7AhWxsrwndwQi06XAqX5JyvKmpaUhMDAQnp6eOHbsGL766iscOHAAmzZtEqt5IiIiyanMVKLcpCRJWd7du3ejSZMmCAoKAgA0atQI69evh0qlvE9KRERESiZJWd5Zs2bB1dUV8+bNw08//QRbW1sMGjRI+0HAYJoCMeNSJVioHskdgYqkP+RrQSQbBW7gI0lZ3szMTMTFxaFt27Y4cOAAVq5ciS+//BIbNmyoiuaJiIgkYdJT/SX9uyxv9+7d0aZNG/j7+wMAWrZsiREjRuD777/H22+/rfcc+sry2v1ztyriUgXY1ede/cbCQoEjDiKSjyRlef/zn/+U6sQ1Gg0EQSjzfCzLS0RERk+BZXlFG/GXLMv77rvvIiUlRVuWd/Dgwfjiiy+wdu1ajB49GomJidiyZQvGjBlT5vmCgoIwatQonftU6bwKwFiYqbiBj7GwtuR2HMakMJ/VEk2KAi/nk6ws75YtW/DRRx/hs88+g42NDYYNG4aRI0eWeT69ZXnTxUpLRERkmiQry9uuXTvExsaK2RwREZGspF6YJwZFzRGqHJzljkBF0h41lTsCFXmUf0PuCFQC9+o3MQqc6udfKBERkQlR1IhfuHtN7ghUxP65ZLkjUJHqdpZyRyAyXWbKGz8rquMnIiIyJioFTvWz4yciIqooLu57rLCwEIGBgWjYsCEWL14MAEhISEBUVBRu3boFBwcHDBw4EBMnToRZeaZJ/nV5H8mHe/Ubj4c5hXJHoBKsrDieIuNWJX+hK1euxIkTJ9CwYUMAwIULFzBjxgwsX74c3bt3x/Xr1zF27FjY2dlh9OjRVRGBiIio6nGqH/j999/xww8/oHfv3tr77ty5g6FDh6Jnz54AgGbNmsHHxwfHjx8vV8fPy/mMx/G7teSOQFopcgcgMllKvI5f1OWIqampmD17NpYuXQpbW1vt/b6+vnjvvfe0P+fl5eHAgQNo1aqVmM0TERHRU4g24tdoNAgNDcWoUaPQsmXLMo/LysrCO++8AxsbGwQGBorVPBERkfQUWB1TtI4/OjoaVlZWT9x//9q1awgJCUHt2rWxefNm2Nvbl3msvrK89mZcNGMsWtWROwEVOyJ3ANKhVhfIHYGkZMrf8X/99ddITk6Gh4cHgMfT+QDw448/4sSJEzh48CCmTZuGwYMH491334WFxZObjo6OxsqVK3Xuu3xioVhxiYiITJJoHf/evXt1fp45cyYAYPHixThz5gyCg4OxYMEC+Pv7G3Q+fWV5hdR14oSlSrOrnyZ3BCriWMNa7ghUQu261eSOQBIy+cV9ZVmzZg0KCgoQEREBNzc37W3MmDFlPsfKygr29vY6NyIiIqNirhLnVg4ZGRmYMWMGOnXqhA4dOmDixIlITjZ8G/Uq+9K8eOMe4HHHT0RERJU3efJk1KxZE/v27YOZmRnee+89zJ07F9HR0QY9X1mr5f612I/kY2OeIXcEKlKrRiO5I1AJudn5ckcgKUk81X/hwgWcPXsWv/32m3Ym/MMPP0RKiuH7eSir4yciIjIiYhXp0Xclm5WVFaz+tVX9uXPn4OLigq+++gpbt25Fbm4uunXrhrCwMIPbUlbHb19T7gRU5G5uG7kjUJHb927KHYFKKMjXyB2BpCRSWV59V7JNmjQJkydP1rkvMzMTly9fRuvWrbFr1y7k5eVhxowZCAsLe0an+omIiJ5B+q5k+/dov+R9s2fPhrW1Nezt7TFlyhQMHjwY2dnZqFbt6VeVsOMnIiKqKJFG/Pqm9fVxcXGBRqNBfn4+rK0fX8qr0TyeZRIEwaC2JCvLu2fPHqxcuRL37t2Dk5MTAgMDMWzYsPKdOCuzCtJSRTjXPS93BCpiZ8ttFI0Jd+4zMSJ1/Iby9PRE48aNMWvWLCxatAiPHj3CsmXL0KtXL4Mve6+SxMVleYv99ddfmD17NhYtWoRTp05h0aJFiIiI0DmGiIiInszS0hKff/45zM3N4evrC19fXzg7O2PhQsN3tpWkLO+NGzdQUFAAjUYDQRCgUqlgbm5u0LSGjlosy2ss0h41lTsCFcnJTZU7ApHpkmHnvnr16mHZsmUVfr6oHX9xWd6oqChs3LhRe7+Xlxfat2+PYcOGwdzcHIWFhQgLC0Pbtm3FbJ6IiEhaEk/1i0G0xE8qy6tWq9GoUSNs2LABZ8+eRXR0NFasWIFff/1VrOaJiIjIAJKU5V2xYgWsrKzg6ekJAOjRowf69OmDL7/8El5eXnrPp28zg2q3r4sVlyrJodUtuSNQESvL6nJHIDJdChzxS1KWt0OHDnBwcNBt2MIClpaWZZ5P32YGl74aLlZcIiKiyjPljv9JZXm3b9+O8PBwvPbaa/Dy8sLx48cRHx+PpUuXlnk+fZsZgGV5jUZWQV25I1ARdX6W3BGISEEk2cAnICAAeXl5CA8PR0pKCho0aIAFCxagZ8+eZT5H32YGAhcvExGRMVHgiF8lGLrVjxHIDukldwQq8mDxV3JHoCLO2fFyR6ASPrnQVe4IVCS0Z/Mqb0NzYJoo5zHr8T9RzmMIbtlLRERUUQoc8SsvMREREVWYokb8lq615I5AZHRUVrZyR6ASrCzN5Y5AUpJh577KUlTHT0REZFQUONWvqI6/4HqG3BGoSIFgLXcEKiI8uC93BCJSEFE/qnz33Xd48cUX4ebmpr2FhobqHJOcnAxPT0/ExcWJ2TQREZH0zMzEuUlI1BH/+fPn0a9fPyxatEjv4xqNBtOnT0d6erqYzRIREclCpTLxqf7z58/j1VdfLfPxVatWwdnZGfXr16/Q+W0C3CsajUR2OfWR3BGoSOPGL8odgUp4+Ge+3BGInki0jl+j0eDixYuwtbVFTEwMCgsL0b17d0yfPh01a9bEkSNHsGfPHuzcuRN+fn5iNUtERCQfU17cl5aWhhdffBG+vr6IjIxEeno6wsLCEBoaikWLFmHWrFmIjIxEtWrVKtxG/uHLYsWlSmo42kbuCFRESLstdwQqobrd83JHICmZcsdfp04dxMbGan+2tbVFaGgoAgICMG3aNIwcORKtW7c2+Hz6yvKWXcuPiIiIDCHaR5VLly7hk08+Qcmt/9VqNVQqFY4cOYJVq1bBw8MDHh4eSEpKwvvvv4+goKAyzxcdHQ13d3edGxERkVExU4lzk5BoI34HBwfExsaiZs2aGDVqFJKTk/Hxxx9j0KBBiIiI0DnW29sbkyZNwsCBA8s8n76yvJbH5ogVl+iZobKwevpBJJmHOVzcZ1JMearf2dkZ0dHR+N///ofVq1fD2toaffr0KXUdv6H0leXViBGUiIhILKbc8QNAx44dsW3btqcet3///gqdv/DavQo9j8RXxzNT7ghURHiYK3cEKsGxBne1JOOmqC17iYiIjIqpj/iJiIhMCjv+qmXh6yV3BCryZypLwRqLF2r7yh2BSriRlCJ3BKInUlTHT0REZFRMfcSfkZGBhQsX4uDBg9BoNOjQoQMWLFiAunXr4uzZswgPD0diYiIcHR0xYcIEBAQElOv86i37xIxLlVB/4mi5I1CROtnfyB2BSqhp31HuCCQlia/BF4OoH1UmT56MnJwc7Nu3Dz///DPMzc0xd+5cZGZmYty4cejfvz+OHz+OiIgILFq0COfOnROzeSIiInoK0Ub8Fy5cwNmzZ/Hbb7/B3t4eAPDhhx8iJSUFP/zwAxwcHDB8+HAAQJcuXeDn54fY2Fi0bdtWrAhERETSMuWp/nPnzsHFxQVfffUVtm7ditzcXHTr1g1hYWG4cuUKXF1ddY53cXHBjh07ytWGVf/OYsWlSsrOL5Q7AhXR1G4mdwQqwdpSeR0BVYICO37REmdmZuLy5cu4ceMGdu3ahd27d+PevXsICwtDdnY2bG11V4Hb2NggJydHrOaJiIjIAKKN+Iu31509ezasra1hb2+PKVOmYPDgwRg4cCDy8vJ0js/Ly3tiiV591fmq2fESMmNxJZUf2ozFf2rUlTsClZCczveGSTHlEb+Liws0Gg3y8/+/QIVG83h3/RdeeAFXrlzROT4xMRHNmzcv83yszkdEREZPZSbOTUKitebp6YnGjRtj1qxZyM7ORlpaGpYtW4ZevXrh9ddfx/3797Fx40bk5+fjyJEj+OabbzBo0KAyzxcUFISTJ0/q3IiIiIyKAjt+0ab6LS0t8fnnn2Px4sXw9fXFo0eP4O3tjdmzZ6NGjRpYv349IiIiEBkZiVq1amHOnDno3LnsxXp6q/Md+EOsuFRJHXvUlDsCFakpnJA7ApXQqG5LuSMQPZGoG/jUq1cPy5Yt0/tYmzZtDKrcR0REpBgK/I5fWVv2/muxH8nnQkqW3BGoyPNNuOjVmNxO5nvDpKhMfOc+IiIiMm7KGvETEREZE4kX5olBUR2/kK+ROwIVca1lJ3cEKiLc/1vuCFRCXcdGckcgKSmw41deYiIiIqowycryXrp0SVuRz9bWFn5+fggNDYWFheERVA25QxnRv2U5dJI7ApXwiDOTpkWBq/olKcublpaGwMBAeHp64tixY/jqq69w4MABbNq0SczmiYiIpGXKG/g8qSzv7t270aRJEwQFBQEAGjVqhPXr10NVzssgHv34p1hxqZJs3DiqMRbV87ixlTGxtmSpcTJuon3MKFmW18fHB15eXliyZAmcnJxw7tw5uLq6Yt68eejatSt69eqF+Ph4ODs7i9U8ERGR9BQ44pekLG9mZibi4uLQtm1bHDhwACtXrsSXX36JDRs2iNU8ERGR9FQqcW4SkqQsb+fOndGmTRv4+/sDAFq2bIkRI0bg+++/x9tvv633fPrK8tr1ekGsuFRJGkFRV4I+2zQFciegEqwszeWOQFIy5cv5nlSW19XVtVQnrtFoIAhCmedjWV4iIiLxiTZsK1mWd9GiRXj06JG2LO+QIUOwdetWrF27FqNHj0ZiYiK2bNmCMWPGlHm+oKAgjBo1SvfOX2eIFZcqKT0v/+kHkSSed6wldwQqgXv1mxhTvpyvuCyvubk5fH194evrC2dnZyxcuBDNmjXDli1bcODAAXTu3BljxozB0KFDMXLkyDLPZ2VlBXt7e50bERGRMVGpzES5SUmysrzt2rVDbGysmM0RERFROSlqhZbm3gO5I1CROw8fyR2BirS3TJM7ApXQqG4zuSOQlBS4uE9RHT8REZFRYcdftcya1Zc7AhVxtFHUn84zrbBGY7kjUAl3U3PkjkD0RPzXm4iIqKIk3nxHDOz4iYiIKkqBl/OJ1vHHx8dj/vz5OvcVb+Zz4cIFJCQkICoqCrdu3YKDgwMGDhyIiRMnwqw8v7QMLu4zFv+pWSh3BCpidveC3BGohBZN+sgdgeiJROv4+/bti759+2p/vnfvHgYNGoTQ0FBcuHABM2bMwPLly9G9e3dcv34dY8eOhZ2dHUaPHi1WBCIiImlxcd9jgiAgNDQUPXr0QL9+/ZCQkIChQ4eiZ8+eAIBmzZrBx8cHx48fL1fHL2TnVUVcqoCMRzZyR6Ai9Z2byx2BSrh9njv3mRR2/I99/fXXSExMRFRUFABod/IrlpeXhwMHDsDPz68qmiciIpKGAjt+0RNrNBqsXr0a48eP17vNblZWFoKDg2FjY4PAwECxmyciIqInEH3Ef/ToUSQnJ2tL8JZ07do1hISEoHbt2ti8efMT99/XV5bX+qG6jKNJaizSYzyE23/IHYFKqG73vNwRSEoKXNUveuKEhAT4+PjAzs5O5/6DBw8iICAA3bp1w7p161CzZs0nnodleYmIyOipzMS5SUj0Ef/Jkyfx5ptv6tx35swZBAcHY8GCBXpnAvTRV5bXbE+waDmpchxtLOWOQMUKqsmdgEpIZx0LMnKif8y4ffs26tatq3PfmjVrUFBQgIiICLi5uWlvY8aMKfM8LMtLRERGT6US51YBhYWFGDlyJGbOnFmu54k+4j99+nSp+9asWSN2M0RERPKTcVX/ypUrceLECTRs2LBcz1PUlr2FKblyR6AiFmbK25/6WaWyryV3BCrBwlx5i71IeX7//Xf88MMP6N27d7mfy79QIiKiihJpcZ9arUZWVpbO7d9XthVLTU3F7NmzsXTpUtja2pY7sqJG/AIv5zMaVhzVGI8CXlppTKwt+d4wJYJIU/3R0dFYuXKlzn2TJk3C5MmTde7TaDQIDQ3FqFGj0LJlywq1paiOn4iI6Fmk70o2KyurUsdFR0fDysoKI0eOrHBb7PiJiIgqSBDEGfFbWVnp7ej/7euvv0ZycjI8PDwAPN4CHwB+/PFHnDhxwqC2JCvLu2fPHqxcuRL37t2Dk5MTAgMDMWzYsHK1ocniVL+xyMlnWV5jIeSlyh2ByGQJMJe0vb179+r8XHwp3+LFiw0+hyRlef/66y/Mnj0bGzduRPv27XHq1Cm8+eabaN68ufZTCxERkdKINeKHhBdKSVKW94cffkBBQQE0Gg0EQYBKpYK5ublB0xo6uGjGaNhZSvspl57gAS9zNSaONViymqRTnpF+MUnK8np5eaF9+/YYNmwYzM3NUVhYiLCwMLRt27YqmiciIpKEoMCr4kXv+PWV5VWr1WjUqBEmTpyIDh064PDhw5g6dSpcXV3h5eVl8Lmt2zqJHZcqSF2okTsCFVE5OMsdgUrIvsXLK02JRqypfgmJnlhfWd4VK1bAysoKnp6esLS0RI8ePdCnTx98+eWXZZ5H32YGREREVDmij/j1leVNSkqCg4ODbsMWFrC0LLvCm77NDP5c5ClqViIiosqQelW/GCQpy+vt7Y3w8HC89tpr8PLywvHjxxEfH4+lS5eWeR59mxng2Byx41IFZT4qkDsCFcl0cJc7ApVwO5mzk6ZEtFX9EhK949dXljcgIAB5eXkIDw9HSkoKGjRogAULFqBnz55lnkffZgb8VpmIiKhyJCnLCwAjR46s1BaDAAC78hcjoKrBDXyMh415htwRqAQLc17OZ0q4qp+IiMiEaBTY8SsvMREREVUYR/xECqcRyr46hqRXwD0uTAoX9xEREZkQXs5X1TIy5U5ARWq4KOtP51lmZZ4tdwQqoZqto9wRSEJKHPGLmvjixYsYPnw4PDw84OXlhfDwcKjVuqV0k5OT4enpibi4ODGbJiIiIgOI1vFrNBoEBQXB19cXx44dw44dO/Drr79i7dq1OsdMnz4d6enpYjVLREQkGwFmotykJNp8bWZmJlJSUrSldwHAzMwMtrb/f+39qlWr4OzsjPr161eskRyWHyX6N7PEw3JHoBKcHAPkjkASMukiPY6OjggMDMSSJUvQpk0bdO/eHU2aNEFgYCAA4MiRI9izZw/mz58vVpNERERUTqKN+DUaDWxsbDB37lz4+/vj77//xqRJkxAZGYmRI0di1qxZiIyMRLVq1Qw6n1qtLrU+oNrzz4kVlyrJ0YaXkBkLVV2+L4xJwT1ezmdKTHpV/759+5CQkIC9e/cCAJo3b47g4GBERETg/PnzGDlyJFq3bm3w+fRV57v0xVCx4hIREVWaElf1i9bx//PPP6VG6BYWFsjIyMCxY8dw9uxZrFq1CgCQlZWF999/HwkJCYiOjtZ7Pr3V+S5/LFZcIiIikyRax+/l5YWlS5dizZo1GDt2LJKSkrB69WqMHj0aYWFhOsd6e3tj0qRJGDhwYJnn01ud7++bYsWlSrJvnSx3BCrGeklGxcJCeSNAqjiTLtLj4uKC6OhoLF++HDExMahevTr69u2L4OBgsZogIiIyKiY91Q8Anp6e8PT0fOpx+/fvr9D5H51LqdDzSHw5vrXkjkBFaql5masxKSjg4j4ybtx3lYiIqII0pryqn4iIyNSY/FR/VbNoVF3uCFTkcuojuSNQkcaOfF8Yk4c5+XJHIAkpcXGf8hITERFRhYk64r969SoWLlyIs2fPwt7eHkOGDEFQUBDMzMxw9uxZhIeHIzExEY6OjpgwYQICAsq3p7V5y0ZixqVKaF7LsB0YSQK2NeROQGSylDjVL1ri7OxsjBkzBvXr18ehQ4cQGxuL7777DlFRUcjMzMS4cePQv39/HD9+HBEREVi0aBHOnTsnVvNERESS08BclJuUROv4T548idTUVMybNw92dnZo2LAhJkyYgK1btyIhIQEODg4YPnw4LCws0KVLF/j5+SE2Nlas5omIiMgAohbpsbS0hKXl/xdvUalUuH//Pk6fPg1XV1ed411cXLBjx47yNWKhqLWIz7Q7D/PkjkBFnq/G9wWRXEx6qv+///0vbGxssHTpUuTm5uLOnTtYt26d9nFbW1ud421sbJCTkyNW80RERJITYCbKTUqiDRVq1KiBtWvXYtGiRejRoweee+459O/fH+fPn4e5uTmys7N1js/Ly3tiiV59ZXntxApLlWZlrrxPuc+srDS5E1AJBYXOckcgeiLROn61Wo2CggJs3rwZKpUKAPDFF1/AxcUFbdu2xYYNG3SOT0xMRPPmzcs8n76yvH9uKruoDxERkdQ0giB3hHIT9cvBt99+GzNmzIC/vz8uXryINWvWYNKkSfDx8cHHH3+MjRs3Yvjw4Th58iS++eYbREVFlXkufWV5hT0s+GMsnFpbPf0gkoTwiF+ZGZNqNlxzYUo0yuv3xev4raysEBUVhUWLFmHhwoWoXbs2xo4di8GDBwMA1q9fj4iICERGRqJWrVqYM2cOOnfu/MTz/bssL6uPEhGRMTH5EX+HDh0QFxen97E2bdpg27ZtYjZHRERE5aSoOSlVTe4WZyxSctRPP4gk8bwTd7Q0Jtl5BXJHIAmZ9FQ/ERGRqTH5qf6qpnqhhdwRqEhGHiuQGYuURy3ljkAlZOemyB2B6IkU1fETEREZE474iYiITEih8vp96cryXrp0SVuRz9bWFn5+fggNDYVFOfbfF27dFjMuVUKdlryO31g4qY7IHYFKqGnfTO4IRE8kSVnetLQ0BAYGwtPTE8eOHcNXX32FAwcOYNOmTWI1T0REJDmNIIhyk5JoI/6SZXmtrKxgZ2eHCRMmICIiAnZ2dmjSpAmCgoIAAI0aNcL69eu1W/saTM0FZcbC0cby6QcRmaCCQo3cEUhCSrycT7QR/5PK8h4+fBiurq6YN28eunbtil69eiE+Ph7OzixmQUREJCVJyvJqNBrExcWhbdu2OHDgAFauXIkvv/yyVOEeIiIiJTHpqf4nleUtLCxEmzZt4O/vDwBo2bIlRowYge+//x5vv/223vOxLK9xU3M603jwWxejYsGS1SZFiVP9kpTlbd26NY4ePapzvEajgfCETzl6y/KuflWsuERERJVm8tfxl1WW193dHZ9//jnWrl2L0aNHIzExEVu2bMGYMWPKPJe+sryanePFjEuV4S53ANLScG94IjKcZGV5t2zZgo8++gifffYZbGxsMGzYMIwcOfKJ5/t3WV7+80ZERMbE5Ef8TyrL265dO8TGxorZHBERkaxM+jt+KZh7tpM7AhVhWV7jYWXuK3cEKiE794rcEYieSFEdPxERkTEx+an+qibcuiN3BCri6MZryIzF87aH5I5AJVSzfU7uCCQhJU7184JTIiIiE6KoET8REZExMamp/rS0NAwZMgTh4eHo1KkTAODs2bMIDw9HYmIiHB0dMWHCBAQEBAAABEFAVFQUdu7ciYyMDDRs2BDBwcF45ZVXDG6z8Nq9isYlkdXxzJQ7AhXRfP2F3BGoBO8uy+WOQBJSYsdfoan+kydPYsiQIbh586b2vszMTIwbNw79+/fH8ePHERERgUWLFuHcuXMAgE2bNiEuLg5r167FyZMnMXXqVMyYMUP7OBEREVW9co/4d+3ahcjISISGhmLq1Kna+3/44Qc4ODhg+PDhAIAuXbrAz88PsbGxaNu2LR48eIDg4GA0a9YMAODt7Y1mzZrh1KlTaNu2rUFtmzdyLG9cqiJ3sqrLHYGK1GnzotwRqIS/03PljkBFPOvXrPI2lLi4r9wdv5eXF/z8/GBhYaHT8V+5cgWurq46x7q4uGDHjh0AgJCQEJ3Hrl69iitXrqBVq1YVyU1ERCS7QgVO9Ze743dyctJ7f3Z2NmxtbXXus7GxQU5OTqljr1+/jrFjx6Jv377o0KFDeSMQEREZBZMY8ZfF1tYWDx8+1LkvLy8P1apV07lv//79mDlzJgYOHIiwsLAyz6evLK9m159ixaVKcvTidfzGQricKHcEKsHuBXO5IxA9kWgdv6urKw4fPqxzX2JiIpo3b679edWqVYiJicEHH3wAPz+/J55PX1ne4z0aiBWXiIio0pS4ql+0jt/Hxwcff/wxNm7ciOHDh+PkyZP45ptvEBUVBQDYsGEDNmzYgNjYWLz44tMXI+kry2u9baxYcamS7hVq5I5AxRxqyJ2ASkjPYh0LU2LSHb+joyPWr1+PiIgIREZGolatWpgzZw46d+4MQRCwatUq5Obmalf9FwsKCsL48eNLnU9fWd58scISEREp1KVLl7BkyRJcvHgRlpaW6Nq1K2bOnIlatWoZ9PxKdfyXL1/W+blNmzbYtm1bqeNUKhVOnDhRmaaIiIiMjtSL+/Ly8jBmzBgMHjwY0dHRyM7ORlhYGGbNmoU1a9YYdA5FbdmryXwkdwQqYmXOMg9GIytb7gRUglNDG7kjkISknupPSkpCy5YtERwcDHNzc1hZWWHIkCGYMWOGwedQVMdPRET0LNJ3JZu+r7ybNm2KmJgYnfsSEhLKtSeOojr+5H035I5AxYLkDkDF8k8nyR2BSihozoWvpkQj0sut70q2SZMmYfLkyWU+RxAELF++HD///DO2bNlicFuK6viJiIiMiUakL/n1Xcn279F+SVlZWXjvvfdw8eJFbNmyBS1atDC4LUV1/I3Wvi13BCry+8M8uSNQkecnDpM7ApWQksj3BpWfvmn9sty8eRNjx45FgwYNsGPHDoNX8xer8AqttLQ0+Pj44OjRo9r7zp49i4CAALi5ucHb2xvbt2/XPqbRaLBs2TK89NJLcHd3x+DBg3Hs2LGKNk9ERCQ7jSCIcjNUZmYm3nrrLfz3v//FunXryt3pAxUc8Z88eRIzZ87UW5Y3JCQEQ4YMwfHjxxEcHIwWLVqgbdu22LZtG3788Uds374dTk5O2Lx5M4KCgnDkyBFYW1tXJAYREZGsCiW+ni8uLg5JSUn4/vvvsXfvXp3HTp8+bdA5JCvLe+3aNWg0Gmg0GgiCAJVKBRub8l32kjrzi/LGpSriFDVa7ghUJH/7brkjUAkWHbzkjkASEus7fkONGjWq1FqA8pKsLO/QoUPx008/oUePHjA3N4e1tTU+++wzjvaJiIgkJFlZ3vz8fHTs2BFBQUFo0KAB1q1bh5CQEMTHx5d5zn+r1tyxvHGpivyVw/3IjUWzRnxfEMlFiXv1i7b9mq2tLfLydFezlizLO2PGDLz00kto2rQpbGxsEBwcjOrVq5f6jqKYWq1GVlaWzo2IiMiYaDSCKDcpSVaWNykpqdSuRBYWFrC01F/XXd9mBmeGNdd7LBERERlGsrK83t7eWL16NTw8PODs7IwvvvgCKSkp6Nmzp97z6dvMIC+kj1hxqZLa1OFuccZCyORe/cbEtZ293BFIQlKP1sUgSVleAFiwYAGWLVuG4cOHIzc3Fy1atMC6detQr149vefTt5lBulhhiYiIRKDEjl8lCMpZmfBo6UC5I1CRtAkxTz+IJOF8Z53cEaiEHZq35I5ARQJa1K3yNj47fvPpBxlgXIfnRDmPIRS1ZS8REZExUeKqfnb8REREFST1zn1iUFTHr7JWVNxn2r0cw4pJUNVzzsmVOwKVUGDJsrxk3NiTEhERVZASF/dVquNPS0vDkCFDEB4ejk6dOmnvP336NN58802cP39e7/MOHz6MMWPGYN++fWjUqJHB7RX+w018jIWjjf79F0h6Qi5H/MbEzt5c7ggkISV2/BXeue/kyZMYMmSIToU+QRCwY8cOjB49utRmPcVSUlIQFhYGjYbTYUREpGxSl+UVQ4U6/l27dmH69Ok6RXoAYNasWdi+fTtCQkL0Pk+j0WD69OkICAioSLNERERUSRWa6i+rQt8777wDZ2dnHD16VO/zoqKiULt2bQwaNEi7o195WL/s+vSDSBJ3HuY9/SCSxHP1neWOQCWo85Q39UsVp8Sp/gp1/GVV03N2LvsfoGPHjiE+Ph5xcXHIyMioSLNERERGxWQ6/vJKS0vDzJkzsWzZMtjb2xvU8avV6lLrBOzKWDdA0uPiPiOSxfeFMalnz0tdybhJ0vH/8ssvSE1Nxdtvvw0A2oV9ffv2xfjx4zFu3LhSz9FXne/PT1+u+rBEREQGKuTOffr169cP/fr10/58+/ZtvPzyy4iPjy/zcj591fnw64yqjElERFQuSrxAzWg38NFXnU+deF+mNPRvDi9xcZ/R4M59RkVtrcCegExKpTv+y5cvl7qvU6dOeu8v1qhRoyc+TkREpARc3FfFhEcFckegImpNNbkjUBHu3GdcboOvh9GQoNKtEjv+Cu/cR0RERMqjqBE/ERGRMZF6u10xKKrjv/vdNbkjUBHnKfoLMJH0Hu3la2FMnN6ykTsCSUiJU/2K6viJiIiMSaEpdfz6SvImJCQgKioKt27dgoODAwYOHIiJEyfCzOzxUoJdu3YhKioKKSkpaNq0KebOnQs3Nzdx/k9IUudTW8gdgYq8+JA79xkTa3OV3BGInqhCi/v0leS9cOECZsyYgSlTpuDEiRNYu3Yt4uLisHHjRgDA0aNH8eGHH2Lx4sU4fvw4+vbtiwkTJiCXK5KJiEihNBpBlJuUyj3i37VrFyIjIxEaGqpTme/OnTsYOnQoevbsCQBo1qwZfHx8cPz4cYwePRrbt29Hnz594O7uDgAIDAzEl19+ie+++w6DBg0yqO3GwZwdMBYXsjnKNBbuIX3kjkAlXLyZIXcEKtLruVpV3oYSF/eVe8Tv5eWFffv24bXXXtO539fXF++9957257y8PBw4cACtWrUCACQmJsLVVbesrouLCy5dulSR3ERERFQB5R7xl1WSt6SsrCy88847sLGxQWBgIAAgOzsbtra2OsfZ2NggJyenvBGIiIiMAlf1A7h27RpCQkJQu3ZtbN68Gfb29gAAW1tb5OXp7u+el5cHR0dHvefRV5bX7PAdseNSBf33FS5gMhbCketyR6ASWrk4yB2BJKTEjl/UnfsOHjyIgIAAdOvWDevWrUPNmjW1jzVv3hxXrlzROT4xMRHNmzfXe67o6Gi4u7vr3IiIiKhyRBvxnzlzBsHBwViwYAH8/f1LPe7v74/g4GC8+uqrcHd3R2xsLFJTU+Hj46P3fPrK8tqceV+suFRJfz/iJiXGwrmMD88kj/Qc1hQxJUoc8YvW8a9ZswYFBQWIiIhARESE9n53d3fExMSgS5cumD9/PhYsWIB79+7BxcUFa9euhYODg97z6SvLy2KXRERkTDSFJtbxlyytu2bNmqce369fP/Tr168yTRIREVElKGrL3lvz98kdgYrt4NcuxiJv3fdyR6CShgXInYAkJGiUNxetqI6fiIjImJj0d/xSaDDsBbkjUJGLhcr7lPussnn7VbkjUAnZaflyRyAJKbHjF/VyPiIiIjJuihrxExERGRMljvglLcubkJCAFStW4Pbt23ByckJQUJDea/7LUnD7YUXjksga2vO1MBbCuStPP4gk4/i81dMPomeGyVzOd/LkScycOVNvWd7ly5eje/fuuH79OsaOHQs7OzuMHj0aR44cwcyZM7F8+XK89NJLOHr0KMaOHQtXV1e0bdtWtP8hIiIiKptkZXk3btyIN998E927dwcAdO7cGTt37kTdunUNbjvvJkeZxqJAYy13BCqWkSl3AiohvTZLVpsSJU71S1aW99y5c3BwcMC4cePQqVMn9OvXDzdv3ixz5z4iIiJjJ2gEUW5SKnfH7+TkBAuLJ08UZGVlITg4WKcsb2ZmJtatW4cJEybg8OHDCA4OxtSpU3H27NkKBSciIqLyk6wsr5WVFQYNGgQ3NzcAQO/evdGlSxckJCSgXbt2pc6jryxv9e6NxY5LFXSXRXqMhnOXLnJHoJKS5Q5AUtIocOc+ycryNmvWrFRHXlhYCEHQP8XBsrxERGTsNBpBlJuUJCvLO2zYMHz44Yfo1q0bOnfujH379uHo0aOYNm2a3vPpK8ur2hMsVlyqJDtLc7kjULEs7hRHRIaTrCzvoEGDYGZmhkWLFuH27dto2LAhli1bpl3892/6yvIWihWWiIhIBCZzHX+x8pblHTBgAAYMGFCZJomIiIyGEi/nU9SWvYUpuXJHoCI5+Zx/MRbC3zfkjkAlONbnzn2mRIkdP4v0EBERmRBFjfizT92TOwIVsQvk4j6jkZUtdwIq4XYKXw+j0cypypuQevMdMSiq4yciIjImnOonIiIioyZqWd7Y2Fhs2rQJKSkpcHJywptvvokRI0YAAARBQFRUFHbu3ImMjAw0bNgQwcHBeOWVVwxu89GDRxWNSyLj4j7jIWRyatmY1HqOu1qaEpO5nE9fWd79+/fj008/xfr169G6dWucO3cOI0aMgIuLCzp37oxNmzYhLi4Oa9euRdOmTfHzzz9jypQpaNCgAcvyEhGRIilxy17RyvJ6e3tj//79sLe3R0FBAdLT06FSqVCjRg0AwIMHDxAcHIxmzZppj2/WrBlOnTplcMf/8BbL8hqLpjX+kDsCFeFlrsbFwpzfoJJxK3fH7+XlBT8/P1hYWOh0/ABgb2+Pa9eu4fXXX0dhYSFGjRqFF198EQAQEhKic+zVq1dx5cqVMnfuIyIiMnZKXNxX7o7fyenJl0c0btwYZ8+exaVLlzBx4kTUqlUL48aN0znm+vXrGDt2LPr27YsOHTqUNwIREZFRMImO/2ksLS0BAG3atMGbb76Jb775Rqfj379/P2bOnImBAwciLCyszPPoK8v7/EjODhiLqw9elDsCFWnR/nm5I1AJdlbc44KMm2gd/8aNG3HmzBksX75ce59ardYpzbtq1SrExMTggw8+gJ+f3xPPFx0djZUrV+rcd35yO7HiEhERVZpJj/g9PDzwySef4LvvvsMrr7yC06dPY/PmzZg/fz4AYMOGDdiwYQNiY2O13/s/id6yvNvGihWX6JmhqldX7ghUQuKdTLkjULH/1K7yJgQZLudLTU3F3LlzcezYMZibm6Nv374ICwuDhYVhXbpoHX/r1q0RGRmJ5cuXY86cOWjYsCFmz56N1157DYIgYNWqVcjNzcXw4cN1nhcUFITx48eXOp++srysOk5ERMZEjhH/lClTUK9ePfzyyy+4f/8+JkyYgI0bN2LMmDEGPV+0srzA40v0vL29Sx2nUqlw4sSJyjQFADCrzqpXxiKbG/gYDeFestwRqAQ13xtUhf7++28cO3YMhw4dgq2tLRo3boyJEyfi448/lqbjJyIiMmVSj/ivXLkCBwcH1KtXT3tfs2bNkJSUhAcPHmj3znkSdvxEREQVJIi0c5++K9n0feWdnZ0NW1tbnfuKf87JyXn2Ov7bn52VOwIVcerDr12MhXCHU/3GxK1L1S8oo2ePvivZJk2ahMmTJ+vcZ2dnh9xc3d06i3+uVq2aQW0pquMnIiIyJmKt6td3Jdu/R/sA0Lx5c2RkZOD+/fuoU6cOgMc74To7O6N69eoGtaWojr/BsBfkjkBFHlhylGksVA15OZ8xseJe/SZFEOk7fn3T+vo0adIE7u7uWLhwIT744AOkp6cjKioK/v7+BrdV4b/QtLQ0+Pj44OjRo9r7YmNj0bt3b7i5uaF3797YsmWL9jGNRoNly5bhpZdegru7OwYPHoxjx45VtHkiIiKTFBkZiYKCArz88ssYPHgwunXrhokTJxr8fMnK8m7btg0//vgjtm/fDicnJ2zevBlBQUE4cuQIrK2tKxKDiIhIVnJs4FOnTh1ERkZW+PmSleW9du0aNBoNNBoNBEGASqWCjY1NudoW8nh9rLHIKagldwQq4mjgbl0kjWv3s+WOQEVeauhQ5W2INdUvJcnK8g4dOhQ//fQTevToAXNzc1hbW+Ozzz7jaJ+IiEhCkpXlzc/PR8eOHREUFIQGDRpg3bp1CAkJQXx8/FPPqQ3bwLBLFajqaQSOMo2F6vn/yB2BSuK6V9NSKM51/FISffmppaUlLC0ttWV5v/32WwDAjBkz8NJLL6Fp06awsbFBcHAwqlevjr179+o9j1qtRlZWls6NiIjImAgaQZSblCQry5uUlFRqVyILCwtYWlrqPZ++zQz+XOQpVlwiIqJKk2NxX2VJVpbX29sbq1evhoeHB5ydnfHFF18gJSUFPXv21Hs+fZsZ5M0fKFZcqiQz3wK5I1CxpDtyJ6ASHB24qyUZN0nK8gLAggULsGzZMgwfPhy5ublo0aIF1q1bp1NooCR9mxnkiBWWiIhIBCaxqr8kQ8vyAo/3EJ4zZw7mzJlT4fZULMtLVIqQy4/ExsTRWf/Xl/SMEqlIj5S4tyQREZEJ4TVZREREFWTSi/ukIDxUP/0gIhOjqsciPcZErcDruqnilPgdP6f6iYiITEiFR/xpaWkYMmQIwsPD0alTJ53HkpOT0b9/f0yfPh0DB5a+BO/w4cMYM2YM9u3bh0aNGhncpo2PS0XjkshSc5X3KfdZZfg7iKSQksWZSVOixKn+Co34T548iSFDhuhU5yum0Wgwffp0pKen631uSkoKwsLCoFHgSkgiIqKSlLhzX7k7/l27dmH69OmlCvQUW7VqFZydnVG/fv1SjxV/KAgICCh/UiIiIqo0UavzHTlyBHv27MHOnTvh5+dX6rlRUVGoXbs2Bg0ahKioqHKHffTLjXI/h6pGvZc4nWkshCOJckegEpzacr8Rk6LAxZyiVedLTU3FrFmzEBkZiWrVSlfRO3bsGOLj4xEXF4eMjIxyByUiIjI2SlzVL8rlfIIgYMaMGRg5ciRat25d6vG0tDTMnDkTy5Ytg729vUEdv1qtLlXUx9ySFyEYCwuzR3JHoGJ2tnInoBLsLM3ljkASUuLiPlE6/n/++QfHjh3D2bNnsWrVKgBAVlYW3n//fSQkJOC1115Damoq3n77bQDQLuzr27cvxo8fj3HjxpU6p77qfGeGNRcjLhERkckSpeNv0KABzp8/r3Oft7c3Jk2apL2cr1+/ftrHbt++jZdffhnx8fFlXs6nrzofPhkqRlwiIiJRmOxUf1XQV50vV6YsVFpOQS25I1CROvWd5Y5AJeTkF8odgSRkclP9/67OV9L+/fvLfKxRo0ZPfC4RERFVDaMd8etj0ai63BGoyJ2HeXJHoCLPcXGfUeHOfSZGgZvRKarjJyIiMiYmN9UvNU0mLyEzFg2r28gdgYrd4uoXY2JhzsuOybgpquMnIiIyJlzVT0REZEI41V/FzOvYyR2BithbJssdgYrlcKrfmDg6KeqfVTJB/AslIiKqKK7qr1pmtUsX/yF5ZOXXlTsCFalVw17uCFTC7XTOwBiN56q+CU71ExERmRAlLu7jdSdEREQmRCUIgvI+riiYWq1GdHQ0goKCStUiIGnxtTAefC2MB1+LZx9H/BJTq9VYuXIl1Gpu6yk3vhbGg6+F8eBr8exjx09ERGRC2PETERGZEHb8REREJoQdv8SsrKwwadIkLpoxAnwtjAdfC+PB1+LZx1X9REREJoQjfiIiIhPCjp+IiMiEsONXqOTkZOTk5Mgdw6T9/fffckeoEoWFhbh165bcMcpFiZnLy9j/H2/cuCF3BDKQ4jr+zMxMLFiwAN27d0f79u3h5eWFsLAw3L17V5L2R44ciRUrVpT7MTHdv38fvr6+SEtLAwCsWLECI0eOrNI2c3NzMWTIEMTFxel93JhfF0ONGTMGa9asKfPxFi1a4OjRowCAJUuWYPXq1XofE9vWrVvh6+sLNzc3+Pr6IjY2tsxjvb290aZNG7i5ucHNzU37WixZsgQaA6uITZ06Fbt37zbo2Li4OHh7e5f7MbGVzHz79m20aNECt2/fFr2dR48e4cMPP0TXrl3h5uaGwYMH4/fff3/q84zpdTFUfHw8+vTpU+bjM2fOxMyZMwEAf/zxB15//XW9j1WVwsJCjBw5ssrbeRYpruOfOnUq0tPTsWPHDpw5cwa7d++GWq3GqFGjUFBQIHc8SeTl5Uk62r9y5QqGDx+OM2fOlHnMs/C6xMTEYPz48QYdm56eXsVpHvvxxx/xv//9D0uWLMGpU6ewePFiLF++HAkJCWU+5/3338fp06dx+vRpnDlzBuvWrcPu3buxcuVKg9qU6v9NTFJlXrZsGc6ePYvdu3fj5MmT6NevHyZOnIjs7OynPldpr0vfvn2xZ88eg459+PAh8vPzqziRrpUrV+LEiROStvmsUFzHf/LkSfj4+MDJyQkAUKdOHcyaNQvt2rXDgwcPAABZWVn44IMP0L17d3Tp0gVTp07F/fv3Afz/aODzzz9H165d4e7ujtDQUGRlZQF4vF3lkiVL8Oqrr8LNzQ1dunTBhx9+iPJe/CAIAjZv3gxfX194eHjgjTfewIULF7SPe3t7Izo6Gv3794ebmxv69++PI0eOaB//448/MGzYMLi5uaFfv35YvXo1vL29UVhYqP1k/frrr+O7774DAGRnZ2POnDnw8vJCp06dsGzZMoN/n61atcLBgwcBAHfv3kWnTp2wbds2AMDvv/+Ot956CwMGDECDBg2eeB5jfF22bNmCfv36aX+Oi4tDixYtcPXqVQDAgwcP0Lp1a9y6dUtn1iA/Px+LFi1Cp06d0LlzZ8TExGjPsWrVKnzzzTf45ptv0LdvX+39hw8fRr9+/eDm5gZ/f3/89ddfT/39C4KAsWPHYujQoSgsLATweDbB19cXWVlZuHfvHsaOHYv27dtDpVLBzc0NnTp1wvHjx5967mItWrRAhw4d8McffwB4/Lv89NNP8fLLL6Njx44YO3as9muL2bNn48SJE4iOjtZ+CNq/fz+GDh2KLl26oF27dhgxYkSFpnUvXryIkSNHokOHDujduzc2btyoff1WrFiBkJAQTJ8+HR4eHnjppZewdOlS7XPz8vIwf/58dOzYEd27d8fy5cvh7e2No0eP6s0MAN988w1effVVtG/fHoGBgbh3795TM6rVavTr1w9TpkzR3vfOO+/gjTfeQEFBAUJDQ/H555/DyckJeXl5yMjIQPXq1WFpaVnu34ccr0tmZiZatWqFP//8E8DjGYy2bdvi448/1h4TEhKCTz/9tNSswU8//YQ+ffqgffv2CAoK0n4QuXXrFsaOHQsAcHNzw+nTpwEAqampCAkJQadOneDl5YUtW7YY9HvZs2cPWrdujUuXLgF4/G9h27ZtcejQIe0xv//+O3744Qf07t3boHPSvwgK89577wn//e9/hfnz5wt79uwRbt++XeqYyZMnC6NHjxbu378vZGVlCXPmzBGGDBkiaDQa4datW4Krq6swYsQIITU1VUhOThYCAgKE6dOnC4IgCJ999pnQp08f4d69e4IgCMKpU6eEF198Ufjtt98EQRCEESNGCJGRkXqzlXxsy5YtQo8ePYQ///xTUKvVwvbt2wUPDw8hJSVFEARB6Nmzp+Dj4yPcuHFDyMnJEcLCwgRfX19BEATh4cOHQpcuXYTly5cLjx49Ei5duiT06NFD6NmzpyAIgvb/4datW4IgCEJkZKTQokULYffu3YJGoxF+//13oUWLFsKpU6cM+p2uWLFC8PLyElJTU4Vhw4YJ06ZN0z6WlpYm5OXlaTPv3LlTUa/LP//8I7Ro0UK4e/euIAiCMHXqVKFt27bCpk2bBEEQhPj4eKFv376lzrF8+XKhd+/ews2bN4Xs7GwhNDRUcHV1FY4cOSIIgiCEhYUJYWFh2nZcXV2FIUOGCCkpKUJubq4wZswYYfTo0Qb9/u/fvy907dpV+Oyzz4RDhw4J7dq1E/78888yj+3YsaOwa9cuvY//+zVSq9XCkSNHhA4dOgibN28WBEEQFi9eLPTv31+4efOmkJeXJ6xYsULw9vbWvs4lfw///POP0Lp1a+Gnn34SBOHx38Mbb7yhfV127typ/bv8t5KP3b17V3B3dxe2bNkiqNVq4cqVK4KPj4+wdetWQRD+/294165dQkFBgXDgwAGhRYsWwunTpwVBEIS5c+cKAwYMEJKSkoSsrKxSr0fJzMV/S8HBwcKDBw+EjIwMoX///sLcuXOf/mIIgpCYmCi0a9dO2LNnj7Bt2zahU6dO2r+fYtu2bRNatGghtGrVSvj++++fek5jel0CAwOFNWvWCIIgCIcOHRLatm0r9O/fXxAEQXj06JHg5uYm/PHHHzrnuHr1qtCqVSvh66+/FvLz84V9+/YJL7zwgvY9cOTIEcHV1VXbRlhYmNC6dWvh8OHDgkajEeLi4nTeh08zc+ZMwc/PT8jIyBB69+4tLF26VPvY/fv3hZ49ewp//vlnqfchGUZxI/7w8HDMmzcP//zzD+bNmwdvb2/4+PggPj4ewONPmQkJCZg9ezZq166NatWqYdasWTh//jwuXryoPc97772HWrVqwcnJCSEhIdi7dy/UajUGDx6MjRs3wsnJCcnJycjLy0O1atUMGi2UFBsbi6CgILRs2RKWlpbw9/dHs2bNtDkBwN/fH88//zxsbW3h5+en/bS+f/9+mJubY/LkybCyskKLFi0wZsyYJ7bXvHlz9OvXDyqVCp07d0adOnVw8+ZNg7JOnDgRTZo0gb+/P1JTU/HBBx9oH3N0dIS1tfVTz2Gsr4uzszNatWqFX375BRqNBr/99huGDh2K3377DcDj37WPj0+p53399dd4++230bhxY9jZ2WHOnDlQqVRPbGvUqFGoU6cObGxs0KtXL4N//7Vr18aSJUuwatUqhIWFYdasWWjZsmWp41JSUjB27Fi0bt1a5/vUf3v//ffh4eEBDw8P7czIqFGjMGLECAiCgG3btmHatGlo3LgxrK2tERwcjPz8fBw4cKDUuWrVqoU9e/bA29sbWVlZuHv3LhwdHcv9foiPj0ezZs0wfPhwWFpawsXFBW+//bbOeoUmTZqgf//+MDc3R/fu3eHk5IQbN24gPz8f8fHxmDp1KurXr49q1aph3rx5MDc3f2Kb48ePR/Xq1VGzZk1069bN4NejWbNmmD17Nj744AMsXrwYH3/8MerVq6dzTP/+/XH+/HksWbIE06dPx8mTJ596XmN5XXr16qUdPf/6668YMmQILl++jLS0NBw5cgSOjo544YUXdJ7z3XffoXXr1ujbty8sLCzQq1cv9OzZ84ntdO3aFZ6enlCpVOjTpw8EQTB4ceLcuXOhVqsxYMAAODk54Z133gEAaDQahIaGYtSoUXrfI2QYC7kDlJeZmRn69euHfv36QRAEXL16FV9//TVmzJgBJycnVKtWDQAwePBgneeZm5vj9u3bcHBwAAA8//zz2sfq168PtVqNjIwMaDQafPDBBzh+/DicnZ3x4osvQhAEgxfgFLtz5w6WLFmCTz75RHtfQUEBWrdurf25Tp062v+2sLDQTnvevXsXDRo0gJnZ/38ua9y48RPbK/7/KmZlZaWdOn4aMzMzDBs2DFOnTkVwcLD2d1gexvy6+Pj44NChQ3B1dYWDgwMGDBiA4cOHIy8vD4cOHcLEiRNLPSc5ORn169fX/lyjRg3UrFnzie2UfA0sLS0N/v0DgKenJxo3boykpCS88sorpR4/c+YM3nnnHXh4eGDRokWwsCj7rTt//nwMHDhQ72OpqanIycnBO++8o/P3lZ+fjzt37pQ63tLSEt9++y22bdsGlUoFV1dXZGVlPbF9fe7cuYOLFy/Cw8NDe59Go9HpvIu/JirZtkajQUZGBnJzc9GwYUPtY/b29nB0dHxim5V5Pfz8/PDJJ5+gTp066Ny5c6nHiz8M9+nTB7t378b3338Pd3f3J57TWF6XXr16YdGiRXj48CF++eUXLFy4EMeOHcORI0dw9OhRvdPn9+7dK/VV33PPPffEdQclf//FuwAa+hrY2dlh0KBB+OSTTxAcHKz9O4mOjoaVlVWVL2Z+1imq4//ll18QEhKCn3/+GQ4ODlCpVHBxccG7776Lw4cP66ws/f7773X+IUlMTETjxo2RkpIC4PEfctOmTQE8/n7Z1tYWjo6OmDBhAmrWrIlff/0V1tbW0Gg06NChQ7mzOjs7IyQkRGdV7M2bN0t10Po0aNAASUlJEARBO8pMSkoqdwZDZWRkYMmSJRg0aBBiYmLg4+NT6hP/kxj769KrVy/ExMTA1dUVXl5eaNmyJWxtbRETE4M6deqgefPmpZ7j7OysMzrJycnBw4cPDf6dlNfatWuRm5uL1q1bY968eVi+fLn2sR07diA8PBwhISEYPXp0pdopnsFZv3492rdvr73/2rVrpUa1wOPXa8uWLdi6dav2Q9mHH35o0PqFkpydndGpUyesW7dOe196erpBi+Jq164NGxsbJCUlaf82cnJyqnSx26JFi/Cf//wHWVlZWL58OUJDQwEAU6ZM0a4ZKKZWqw16Xz+JlK9LvXr10LJlS8TFxeH+/fto06YNvLy88Ntvv+GXX37R+dsr5uzsXGrm4e7duwbNBlbEzZs3sXr1agQEBOCjjz5C165d4ezsjK+//hrJycnaD5B5eXkAHi+C5UI/wylqqr9Dhw6oXbs23nvvPVy+fBn5+fnIyspCfHw8bty4gR49eqBevXro0aMHIiIikJ6ejvz8fKxevRr+/v7aRWYAsHTpUu3iqcjISPTr1w+WlpbIysqCtbU1zMzMkJWVhY8++ghZWVnlXrE6ePBgrF69WruI7JdffkGfPn0MWpTl7e0NQRCwZs0aqNVqXLt2TecfzOI3W/HCt8qaM2cOXFxcsHDhQgwbNgzTpk1Dbm6uwc839tfFxcUFtWvXxpYtW9C1a1cAj0fYMTExZS4OCggIQExMDK5evYpHjx5h8eLFOqMVKysr0T4InD9/HitWrMDixYuxePFi/Prrr9ixYwcAICEhAQsWLMCKFSsq3ekDj2dm/P39sXTpUty9excajQa7du3C66+/rl1IVvL/7eHDhzAzM4ONjQ0EQcChQ4ewe/fucr8f/Pz8cObMGcTHx6OgoADJyckYP348Fi9ebHDmFStW4N69e8jNzcWiRYuq7PX48ccfER8fr309Nm3apP1qyM3NDWvXrsXly5dRUFCA7du34/z58zqLPCtC6tfFx8cHq1evRufOnWFubo6uXbvi22+/hUaj0fngUaxv377466+/8NVXX6GgoAC//vor9u3bp328+N8kMV6D/Px8TJs2DX369EF4eDg6dOiA0NBQaDQa7N27F6dOncKJEydw4sQJvP7663j99dfZ6ZeTojp+GxsbfPHFF3BycsKECRPg4eGBHj16ID4+Hhs2bECzZs0AAB999BFq1KiB/v37o3Pnzjh48CBiYmJ0RprPPfccXn/9dfTt2xdubm6YNWsWgMed4KVLl9CxY0e88soryMrKQrdu3co9wgkMDET//v0xceJEuLm5ISIiAvPmzcPLL7/81Ofa2dkhKioKP/30Ezp27Ihp06aha9eu2pXDderUgY+PD4YMGYKtW7c+9Xzx8fFwc3PT+9jWrVtx9OhRREREAACmTZsGlUql/dkQSnhdfHx8kJWVhY4dOwIAvLy8kJubq/f7fQAYO3Ys+vbtixEjRsDLywvVq1fXGdW99tprOHXqFHr06GFQ+3369NG7R0B2djbeffddjBgxAh4eHqhfvz5mz56NiIgIXL9+HStXrkRhYSFCQkK014C7ublh3rx5BrWrT1hYGNq1a4c33ngDHh4e2LhxIyIjI/Hiiy8CePz99c6dO/HGG29gwIAB8PT0RJ8+fdC5c2esXr0ab731Fq5fvw61Wm1wmw0bNkRMTAy+/PJLeHp6ol+/fmjatKlBHT8AvPvuu2jatClee+01+Pr6wtnZGWZmZtr3RMnMhnBzc9NZb1Ps3r17mD17NqZPn44mTZqgdevWGD9+PGbMmIG0tDS8+eabeOuttzBhwgR06dIF8fHx2LhxI5577jmDfxdlkfJ16dWrF9LT07UfhN3d3aFSqdCrVy+9a1kaN26MNWvWIDY2Fu7u7oiKitJ577i6usLd3R3dunXTXiH0JGvWrClzj4BPP/0U6enp2uvzP/jgAyQmJiI6Ovqp5yUDybOmUD7/XhFvjNLS0oQTJ07o3Ld582ZhyJAhFT7nW2+9VclUVUsJr0tlHDp0SFi7dq3cMRTr2LFjQmZmpvbnhw8fCq6ursL169crdL6tW7cK3333nUjpqLw0Go0QGBgodwyTpagRv6koLCzEW2+9pf3kfPv2bXzxxRdPXUVbltOnTxs8MqWqcejQIfj5+ckdQ7HWr1+PiIgI5OXl4dGjR4iMjMR//vMfNGnSpNznEgQB58+fx0svvSR+UDLIvn374O/vL3cMk2VyZXlv376Nl19+GT/99BMaNWokd5wy/fjjj/j0009x+/Zt1KhRAwMGDMCkSZPKvZpaKZTyupA87t27h/fffx8nT55EYWEh3N3dMXv2bFGm2IlMjcl1/ERERKaMU/1EREQmhB0/ERGRCWHHT0REZELY8RMREZkQdvxEREQmhB0/ERGRCWHHT0REZELY8RMREZkQdvxEREQm5P8Atwz1aDPSf7MAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax = sns.heatmap(X,  # 绘制特征矩阵的热力图\n",
    "                 cmap='RdYlBu_r',\n",
    "                 xticklabels=list(X_df.columns),\n",
    "                 cbar_kws={\"orientation\": \"vertical\"},\n",
    "                 vmin=-1, vmax=9)\n",
    "plt.title('X')  # 设置标题"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e325f50a-6ddc-468e-bc66-23668c1d8760",
   "metadata": {},
   "source": [
    "## 数据矩阵的质心计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8782bbe8-d0cf-4468-8417-4867918bf508",
   "metadata": {},
   "outputs": [],
   "source": [
    "v_1 = np.ones((len(X), 1))  # 生成全为 1 的列向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f63a7932-82ef-4cd6-a102-57537ee5b0f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "E_X = v_1.T @ X / len(X)  # 计算 X 的质心，即均值向量"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f43cf9a-0dcd-40c8-a49f-2275f7b77a3e",
   "metadata": {},
   "source": [
    "## 数据去均值处理（中心化）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1a41d530-3ffe-49b9-b2ba-98c7b33aa801",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_demean = X_df.sub(X_df.mean())  # 将 X 中每列减去其均值，得到去均值后的矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "44bfcb8f-3389-44cb-bcec-36f30e53b235",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$X_{demean}$')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ujODgYLRr1w6HDh3C5MmT4eTkBC8vLzEjEBER6Q0vPiynpUuXwszMDB07dgQAdOvWDX369MHmzZtLLAx0tV1uXvtKpWelUrrIhlZyYd/EWeoIRNUWTyWU071792BjY6N9YBMTmJqWfG40Ojoay5Yt09qW+PemyohHRERULpwxKCdvb2+Eh4ejd+/e8PLyQkJCAuLi4rBo0aISX6Or7fK19Kr3BhiqlvhN6giklvooS+oIRFSF6KUwCAgIQE5ODsLDw5GcnIyGDRti7ty56N69e4mv0dl2OSWzkpMSERGVHlc+LIOibZcBYMSIERgxYkRlHY6IiEjveI2BxOwsM6SOQIUacB0DubCtZyV1BCoiJ18ldQSiCjGowoCIiEhOePGhxLjyoXzYpfJ2RblIffSS1BGoCLZdrl4URkZSRxBd1fuOiIiIqNwMasbg7IOnUkcgtZY1LaSOQGoPT92XOgIVkZaTJ3UE0qOqeCpB1BmDixcvYtSoUWjfvj06deqE6dOnIyUlRWufhw8fomPHjti2bZuYhyYiItI7hZFClIeciFYY5OTkYMyYMXB1dcVff/2F//73v0hLS8OsWbM0+6hUKkybNg2pqaliHZaIiIhEJNqphHv37qFFixYICQnRtFQePHgwpk+frtln+fLlsLe3R4MGDcp1DBf7mmLFpQpSmNpLHYHUnHvyvZCTRjzNVq1I8Wn/4sWLWLhwIS5cuABTU1N06tQJM2fORJ06dUQZX7QZg2bNmiEmJgbGxsaabfHx8WjVqhUA4OjRo9i5cyc+/fRTsQ5JREQkKYWxQpRHaZVmdr6iKuXiQ0EQsGTJEvz555/YsGEDHj9+jFmzZiEyMhI1atQo97h3n+aKmJIqomXNHKkjkFotWy5wJCd3n/J3Qy6cbSwr/Rj6XhK5NLPzFSV6YZCRkYGPPvoIFy5cwIYNG+Dk5IQxY8ZgxIgRaN26danH0dV2mYiIqDornJ0vqujsvBhELQxu3bqFsWPHomHDhti6dSvq1KmDe/fu4fjx40hMTMTy5csBPCsePvvsM8THxyM6OlrnWLraLi/dfUTMuERERBUi1jUGuj4M62wmWMT/zs6LRSEIgiDGQOnp6ejfvz88PT0REREBo+esBuXt7Y0JEyZgwIABJe6j64d0MUuUqCQCV7tzUkcgtWFfc2ZNTj4Y8rrUEUjNu4ltpR/j0bBOoozzg+eQYh+GJ0yYgIkTJ+rcv+js/IoVK+Ds7CxKDkDEGYNt27bh3r17+O2337Br1y6t506fPl3m8XRWSllc4IiIiKqeoKAgjBo1SmtbSbMFumbnxSRaYTBq1Khi31RJ9u7dK9ZhSSJGqTekjkAajaQOQEWwV0L1ItaphBedNiiUnp6O9957r1Sz8+VlUEsiExERyYm+l0QWe3ZeFxYGREREBqIss/PlZVCFgS2n6OQjh2tKyEVONpv2yAmbKFUvVbHtskEVBkRERHIitwZIYhC1MDhy5Aj+85//4Nq1a7C0tMRbb72FsLAwWFhYIDExEeHh4bh69SpsbW0xfvx4BAQEiHl40icTc6kTkFpudr7UEYioChFtDiQlJQVBQUEYOnQoTpw4ge3bt+P48eP49ttvkZ6ejg8++AD9+/dHQkICIiIiMH/+fJw9e1aswxMREemdkbFClIeciDZjUKdOHRw+fBjW1tYQBAFpaWnIzc1FnTp1sHv3btjY2GDYsGEAgA4dOsDX1xcbN26Ei4uLWBGIiIj0iqcSXsDa2hoA0LVrVyQlJcHd3R0DBgzAkiVL4OTkpLWvg4MDtm7dWqbxzydzgSO5aN6ottQRSK12ncpvFENEuun7dkV9qJTLKXfv3o0DBw7AyMgIoaGhyMzMhKWl9j9eFhYWyMrKqozDExERUTlVyl0JFhYWsLCwQFhYGAICAjBixAg8far9aT8nJ+e5LZh19UqwNDGujLhUHmb8lEpEVBVPJYg2Y3Dq1Cm89dZbWn/MlUolTE1N4eDggCtXrmjtf/XqVTg6OpY4XnR0NNzc3LQeREREsmKsEOchI6IVBs7OzsjJycGiRYugVCpx9+5dLFy4EP7+/ujVqxcePXqE2NhY5OXl4ejRo/jll18wcODAEscLCgrCyZMntR5ERERUuUQ7lVCjRg3ExMTgiy++QKdOnVCzZk34+voiJCQEZmZmWLNmDSIiIhAZGYk6derg448/hqenZ4nj6Woo0dY4Say4VEFC2gOpI5BaTvZLUkegIthEqXqpiqcSRL3GwMHBAWvWrNH5XJs2bbBp0yYxD0dERCQtYy6JLKmnebxFTi7qnTomdQTS8JU6ABVxP4N9RGTDzlrqBAbJoAoDIiIiWeGpBCIiIipUFRc4MqjCwNacF7zJBtsuywabKMmLpUnVO+dM1YtBFQZERESywlMJz/e8tssXL17UdFS0tLSEr68vwsLCYGJS+gjnH9mIGZcqoEvvQVJHIDXzUyqpIxBVX1XwVIJe2i6npKQgMDAQHTt2xPHjx/Hjjz9i3759WLdunViHJyIi0juFkUKUh5zope3yjh070LRpUwQFBQEAGjdujDVr1kChkNcPg4iIqLrTS9vlWbNmwcnJCXPmzMEff/wBS0tLDBw4UFMolJaVKZsoyYYyW+oEpJZ2M0fqCETVVxVc4EgvbZfT09Oxbds2uLi4YN++fVi2bBk2b96MtWvXVsbhiYiI9IKnEkrpf9sud+3aFW3atIG/vz8AoEWLFhg+fDh+++03vP/++zrH0NV2uVntx5URl8pBSH8odQRSM6lZT+oIRFSF6KXt8quvvlrsj7xKpYIgCCWOx7bLREQke1Ww7bJoMwZF2y5PnToVycnJmrbLgwYNwvfff49Vq1Zh9OjRuHr1KjZs2IAxY8aUOF5QUBBGjRqlte3UIy7kIhedVbzGQC5MLdnNT06y83n7aLUisz/qYtBb2+UNGzbgyy+/xLfffgsLCwsMHToUI0aMKHE8XW2XkZ4mVlwiIiLSQW9tl19//XVs3LhRzMMRERFJSm4XDorBoJZEPnc7TeoIpNbJw1XqCKSWl/1I6ghUBHslVDNV8FQC/w8mIiIiDYOaMejmZCd1BFIzSj0kdQRSs67zktQRiKovo6r3+dqgCgMiIiI5UVTBUwksDIiIiMqLFx+WTkFBAQIDA9GoUSMsWLAAABAfH4+oqCjcvn0bNjY2GDBgAIKDg2FUhmkY3h8sJ7lSByC1jBSuKSEnFrz4kAxcpRQGy5Ytw4kTJ9CoUSMAwPnz5zF9+nQsWbIEXbt2xY0bNzB27FhYWVlh9OjRlRGBiIio8vFUwosdOXIEu3fvRs+ePTXb7t69iyFDhqB79+4AgObNm8PHxwcJCQllKgzO3k0XOy6Vk9nLg6WOQBp/SB2AqNqqiusYiDrn9fjxY8yePRuLFi2CpaWlZnuvXr3w0Ucfab7OycnBvn370KpVKzEPT0RERBUk2oyBSqVCWFgYRo0ahRYtWpS4X0ZGBj788ENYWFggMDBQrMMTERHpn3HVu6ZEtMIgOjoaZmZmz+1/cP36dYSGhqJu3bpYv349rK2tS9xXV9vl7Fw2UZILlxp/Sh2BSJZyeJF09cJrDEr2888/4+HDh3B3dwfw7HQBAPz+++84ceIE9u/fjylTpmDQoEGYOnUqTEyef+jo6GgsW7ZMa1vounix4hIREZEOohUGu3bt0vp65syZAIAFCxbgzJkzCAkJwdy5c+Hv71+q8XS1Xb6YJYgTlipMePJQ6gikVq9RM6kjUBHNba2kjkB6VBUvPtTLAkcrV65Efn4+IiIiEBERodnu5uaGmJgYna/R2XY562llxiQiIiobnkoovcKFjYBnhQERERHJn0Eticx2pjJy/4HUCUitfmO2wJaTx9l5UkcgtVeszSv/IDyVQERERIXYRElid59yfX65aNGym9QRSO3yBs7eyElON14MWq1UwbbLVe87IiIionIzqBkDIiIiWamCMwZ6a7u8c+dOLFu2DElJSbCzs0NgYCCGDh1apnEb1dTDhSRUKkZ/75M6AqnVrtNR6ghUBFc+rGZYGJTO/7Zdvnz5MmbPno3Y2Fi0bdsWp06dwsiRI+Ho6KhZKZGIiIikp5e2y//++y/y8/OhUqkgCAIUCgWMjY2LL2D0AmcfcIEjuWjV3EXqCKSWnpItdQSi6ou3Kz5fYdvlqKgoxMbGarZ7eXmhbdu2GDp0KIyNjVFQUIAZM2bAxYV/XIiIyIBVwVMJon1Hz2u7rFQq0bhxY6xduxaJiYmIjo7G0qVL8ddff4l1eCIiIhKBXtouL126FGZmZujY8dlFUt26dUOfPn2wefNmeHl56RxPV9tlr1dqihWXKki4e0nqCKRmbsmZNyLJSDhjkJKSgsGDByM8PBweHh6ijauXtsvt2rWDjY2N9oFNTGBqalrieLraLv9+6pRYcYmIiCpOosLg5MmTmDlzJm7duiX62Hppu7xlyxaEh4ejd+/e8PLyQkJCAuLi4rBo0aISx9PZdjmTtwHJRZOXmkodgdRys/OljkBEerR9+3ZERkYiLCwMkydPFn18vSxwFBAQgJycHISHhyM5ORkNGzbE3Llz0b179xJfw7bLREQkeyLNGOg6fa7z7yCeXdDv6+sLExOTSikMFIIgCKKPWklUcWOljkBqRj39pI5AaqoT+6WOQEUYvdFJ6ghUyKp/pR9CtW+KKOMsP/dqsdPnEyZMwMSJE5/7OmdnZ6xfv16e1xgQERFVOyLNGOg6fV7WtX7EwsKAiIhIYiWdNpCCQRUGCte2Ukcgkh2Fra3UEaioPLaHr1a48iERERFpVMGVDw2qMBD++UfqCKSmaNTixTuRXgg3bkodgYpQNG4udQSqRi5dEn+xOVFLnV9//RUtW7aEq6ur5hEWFqa1z8OHD9GxY0ds27ZNzEMTERHpn5GROA8ZEXXG4Ny5c/Dz88P8+fN1Pq9SqTBt2jSkpqaKeVgiIiJJKBTy+qMuBtELg7fffrvE55cvXw57e3s0aNCgXOOndZ1W3mgksjupdlJHIDWXrmlSR6CiLGpInYCoQkQrDFQqFS5cuABLS0vExMSgoKAAXbt2xbRp01C7dm0cPXoUO3fuxE8//QRfX1+xDktERCQdmZ0GEINohUFKSgpatmyJXr16ITIyEqmpqZgxYwbCwsIwf/58zJo1C5GRkahRo/zVtO2tLWLFpQoybdpX6gikJpw9K3UEKkLh0FLqCFSoth6OwcKgZPXq1cPGjRs1X1taWiIsLAwBAQGYMmUKRowYgdatW5d6PF3rRnOCjoiIqHKJVupcvHgRX3/9NYq2XlAqlVAoFDh69CiWL18Od3d3uLu74969e/jss88QFBRU4njR0dFwc3PTehAREcmKkUKch4yINmNgY2ODjRs3onbt2hg1ahQePnyIr776CgMHDkRERITWvt7e3pgwYQIGDBhQ4ni61o3OtbwiVlyqKHbAlg8Lc6kTUFFW+pi/JtngqYSS2dvbIzo6Gv/5z3+wYsUKmJubo0+fPsXWMSgtXetG5xSIkZSIiEgkVbAwMKi2y8KDGKkjkJqiBtfnlwtV4lGpI1ARCudWUkcgNYVdYKUfQzgXLso4ijYfizKOGAxqSWQiIiJZqYIzBiwMiIiIyouFgbQOFvhLHYHUGqh4wZtc1HTrKnUEKqKW6X2pI5CaldQBDJRBFQZERESywhmD50tLS8MXX3yB/fv3Q6VSoV27dpg7dy5eeuklJCYmIjw8HFevXoWtrS3Gjx+PgICAMo3fOWWZmHGpAnLt+0gdgdTMz+yQOgIVoXDpIHUE0mhT+YeQ2RoEYhC11Jk4cSKysrKwZ88e/PnnnzA2NsYnn3yC9PR0fPDBB+jfvz8SEhIQERGB+fPn4yyXciUiIpIV0WYMzp8/j8TERBw+fBjW1tYAgM8//xzJycnYvXs3bGxsMGzYMABAhw4d4Ovri40bN8LFxUWsCERERPrFUwklO3v2LBwcHPDjjz/ihx9+QHZ2Njp37owZM2bgypUrcHJy0trfwcEBW7duLdMxrr/CtstyYZOfLHUEUrNo1U7qCFRUXo7UCaiQqR6OUQULA9G+o/T0dFy6dAn//vsvtm/fjh07diApKQkzZsxAZmYmLC0ttfa3sLBAVlaWWIcnIiIiEYg2Y1C4fPHs2bNhbm4Oa2trTJo0CYMGDcKAAQOQk6NdRefk5Dy3BbOu7oqpOQazSGOVdzmFNwLJRadGTi/eifTGxCRX6gikppd/pThjUDIHBweoVCrk5eVptqlUzzrtvPbaa7hyRbsB0tWrV+Ho6FjieOyuSEREsqcwEuchI6Kl6dixI5o0aYJZs2YhMzMTKSkpWLx4MXr06IG+ffvi0aNHiI2NRV5eHo4ePYpffvkFAwcOLHG8oKAgnDx5UutBREQkK1WwMBC1iVJSUhIWLFiAhIQE5ObmwtvbG7Nnz0atWrVw7tw5RERE4PLly6hTpw6Cg4Of23ZZp4I9YkWlCiowKvk0EOmXUfJFqSNQEQpz/m7IRu3BlX4I4fZyUcZRNAkRZRwxGFR3RRYG8sHCQD5YGMgLCwMZ0UdhcHeFKOMoGo0XZRwxGNaSyHm8qEcuTqZ7Sh2B1NpbcW1+Ocmy5MWgcqGXiw8VXPmQiIiIqjDDmjEgIiKSE5ldOCgGwyoMeCpBNlzqXZU6AqmpjhyVOgIVYfWGsdQRqJCJHpooVcHCoOp9R0RERFRuemu7fPHiRU1HRUtLS/j6+iIsLAwmJqWP8NSipZhxqQJMwfXg5ULZ4V2pI1ARFqokqSOQPnHlw+crqe1ySkoKAgMD0bFjRxw/fhw//vgj9u3bh3Xr1ol5eCIiIv3iAkclO3/+PN59912ttstpaWlITk7GwYMHsXv3bmzatEmz/927d6FQKNCwYcNSH0NI+ESMqCQChVs3qSOQmnDjjNQRqAhFg+ZSR6BCVv0r/RBCcqwo4yjsAkUZRwyilSlF2y77+PjAy8sLCxcuhJ2dHc6ePQsnJyfMmTMHnTp1Qo8ePRAXFwd7e3uxDk9ERKR/VXDGQC9tl9PT07Ft2za4uLhg3759WLZsGTZv3oy1a9eKdXgiIiL9UyjEeciIXtoue3p6ok2bNvD39wcAtGjRAsOHD8dvv/2G999/X+d4utouC215kZVcWClSpY5AakY5vI1XVnhbdfUis0/7YtBL22UnJ6dif+RVKhWed3kD2y4TERHpn2gXH+bl5aFPnz5o0aIF5s+fj9zcXEyePBk1a9bE5MmT0b9/f4SGhmL06NG4evUqxo4dizFjxmDkyJE6x9M1Y2BV47QYUUkEqcqmUkcgtTqZB6SOQEVk13KROgKpWelhgSMh7QdRxlHYDBVlHDHore1yYmIivvzyS1y+fBkWFhYYOnQoxo8fD0UZzq2ohINiRaUKYmEgHywM5IWFgXzoozBA+mZxxtFDJ8jSMqi2yywM5IOFgXywMJAXFgbywcKgfAyqV4Ii5V+pI5Datfy2UkcgtTqPbkodgYqwMjaof1arttrslVAe/D+YiIiovFgYSCujlrvUEUitgbLq/TIYKkVtTl3LSZ7ZS1JHIDVTqQMYKIMqDIiIiGRFZosTiYGFARERUXlVwe6KohUGcXFx+PTTT7W2FS52dP78ecTHxyMqKgq3b9+GjY0NBgwYgODgYBiV4Yda0+iOWHGpgmoaX5M6Aqmp/totdQQqwsSRTZRk45X2UicwSKIVBv369UO/fv00XyclJWHgwIEICwvD+fPnMX36dCxZsgRdu3bFjRs3MHbsWFhZWWH06NFiRSAiItIvXnxYOoIgICwsDN26dYOfnx/i4+MxZMgQdO/eHQDQvHlz+Pj4ICEhoWyFQdaTyohL5fDUoqXUEUitpkdXqSNQURY1pE5A+sTCoHR+/vlnXL16FVFRUQCAXr16oVevXprnc3JysG/fPvj6+lbG4YmIiPSjChYGon9HKpUKK1aswLhx42BtbV3s+YyMDISEhMDCwgKBgYFiH56IiIgqQPQZg2PHjuHhw4eaFstFXb9+HaGhoahbty7Wr1+vs3AopKuJUo1MtvqVizSjl6WOQGo19i+ROgIVYdTZW+oIVKi2Ho5RBe9KEP07io+Ph4+PD6ysrLS279+/HwEBAejcuTNWr16N2rWf/46x7TIREcmewkich4yIPmNw8uTJYq2Uz5w5g5CQEMydO1fnTIIuQUFBGDVqlNY2hRAvWk6qGBuzW1JHoEI2taROQEXV4sqHZNhEL1Pu3LmDl17S/sVYuXIl8vPzERERAVdXV81jzJgxJY5jZmYGa2trrQcREZGsKBTiPMrg8ePHCA4Ohru7Ozw8PBAREYH8/HzRviXRZwxOnz5dbNvKlSvFPgwREZH0JDgNMGnSJNSvXx8HDx7Eo0ePMH78eMTGxj73w3ZZGNSSyELaA6kjkJppw2ZSRyA1xStNpY5AReXnSp2AClXBLko3b97E8ePHceDAAVhaWqJJkyYIDg7GV199VT0LAyIiIlkRacZA1514ZmZmMDMz09p25coV2NjYoH79+pptzZs3x7179/DkyRPUqlXxa44MqzBI4+2KcmHaOFvqCFRImSN1Aioqj++HbOhhxkAQqTCIjo7GsmXLtLZNmDABEydO1NqWmZkJS0tLrW2FX2dlZVXDwoCIiKgK0nUn3v/OFgCAlZUVsrO1P5gVfl2jhjjLcbMwICIiKidBEGfGQNdpA10cHR2RlpaGR48eoV69egCAa9euwd7eHjVr1hQli97aLu/cuRPLli1DUlIS7OzsEBgYiKFDh5bpGEJ6ulhxqYKy8m2ljkBqNW7clDoCFaFowLbL1YkAY70er2nTpnBzc8MXX3yBefPmITU1FVFRUaVeI6g09NJ2+fLly5g9ezZiY2PRtm1bnDp1CiNHjoSjoyPc3d3FikBERKRXYs0YoAxLGURGRmLevHl48803YWRkhP79+yM4OFicHNBT2+Xdu3cjPz8fKpUKgiBAoVDA2Ni4VNMmRSnMLSojLpWDlQkvBJULIZXtyOWEt1XLh8LqxfsYonr16iEyMrLSxtdL22UvLy+0bdsWQ4cOhbGxMQoKCjBjxgy4uLhUxuGJiIj0QhB/AWHJiV4Y6Gq7rFQq0bhxYwQHB6Ndu3Y4dOgQJk+eDCcnJ3h5eZV6bEUbD7HjUjnlqSxfvBPphXlLJ6kjUBGKGrz+pjpRiXUqQUZE/450tV1eunQpzMzM0LFjR5iamqJbt27o06cPNm/eXOI4SqUSGRkZWg8iIiKqXKLPGOhqu3zv3j3Y2NhoH9jEBKamJa8+oWuxh0uJi0TNSkREVBH6vitBH/TSdtnb2xvh4eHo3bs3vLy8kJCQgLi4OCxaVPIfel2LPeSYXhE7LpVTmrKJ1BFIzcpJvNuUqOJMFOyVIBf6uPZQtLsSZET0wkBX2+WAgADk5OQgPDwcycnJaNiwIebOnYvu3buXOI6uxR5yCsROS0REREUpBEEQpA5RWim5/0odgdQe59R/8U6kF441D0sdgYrIgzirz1HFmRq1r/RjZOWfE2UcK5M2oowjBi6JTEREVE6qKni7YtX7joiIiKjcOGNAZOAKFFxTQk7yCvh+yIWpHj768uJDIiIi0uDtihKzMbstdQRSq4q/DIbKODdF6ghUhJU5b1esTqrijIGo39GFCxcwbNgwuLu7w8vLC+Hh4VAqlVr7PHz4EB07dsS2bdvEPDQRERGJQLTCQKVSISgoCL169cLx48exdetW/PXXX1i1apXWPtOmTUNqKjvzERGR4RNgJMpDTkQ7lZCeno7k5GRNa2UAMDIygqXl/1+Is3z5ctjb26NBgwblOoZRbrooWUkEZegdTpUr//vvpY5ARRj79pQ6Aqkp7Cr/GGyi9By2trYIDAzEwoUL0aZNG3Tt2hVNmzZFYGAgAODo0aPYuXMnPv30U7EOSURERCITbcZApVLBwsICn3zyCfz9/XHz5k1MmDABkZGRGDFiBGbNmoXIyEjUqFGjVOMplcpi1ydkGbcTKy5VUF3za1JHIDUjj9ZSR6AiFGa8XbE6qYoXYotWGOzZswfx8fHYtWsXAMDR0REhISGIiIjAuXPnMGLECLRuXfp/wHR1Vzx45oBYcYmIiCqsKt6VIFphcP/+/WKf8E1MTJCWlobjx48jMTERy5cvBwBkZGTgs88+Q3x8PKKjo3WOp6u7YhYyxYpLREREOojWROnq1at45513EBISgrFjx+LevXsIDg6Gl5cXZsyYobWvt7c3JkyYgAEDBpTtIDn/FSMqiUDI4oWgsnH/ptQJqKiXGkqdgNQUdoGVfozknPuijGNnUb6L8iuDaDMGDg4OiI6OxpIlSxATE4OaNWuiX79+CAkJEesQREREslIVTyUYVNtlIeETqSOQmsKtm9QRSE11eJfUEagIozbuUkegQrUHV/ohHmYniTLOS5byaWVvUEsiExERyYmKdyUQERFRoap4KsGwCoMmr0idgNTOpnpKHYHU2jQ4I3UEKsqqttQJSI/ktpyxGKred0RERETlJuqMwbVr1/DFF18gMTER1tbWGDx4MIKCgmBkZITExESEh4fj6tWrsLW1xfjx4xEQEFCm8TPqdhIzLlVAK5NEqSNQIYW91AmIqq2qeCpBtO8oMzMTY8aMQYMGDXDgwAFs3LgRv/76K6KiopCeno4PPvgA/fv3R0JCAiIiIjB//nycPXtWrMMTERHpnQrGojzkRLTC4OTJk3j8+DHmzJkDKysrNGrUCOPHj8cPP/yA+Ph42NjYYNiwYTAxMUGHDh3g6+uLjRs3inV4IiIiEoGoTZRMTU1hamqq2aZQKPDo0SOcPn0aTk5OWvs7ODhg69atZTpGnorNSeTiXtbLUkcgtSam4qy8RkRlx1MJz/HGG2/AwsICixYtQnZ2Nu7evYvVq1drnre01P6jbmFhgaysLLEOT0REpHcCjER5yIloMwa1atXCqlWrMH/+fHTr1g0vv/wy+vfvj3PnzsHY2BiZmdoNkHJycp7bgllX22WY6t6X9M/UKFvqCKQmPPhX6ghUhKLZG1JHIKoQ0QoDpVKJ/Px8rF+/HgqFAgDw/fffw8HBAS4uLli7dq3W/levXoWjo2OJ4+lqu3zkbLxYcYmIiCpMZThdBUpNtF4JSqUSnTp1wvTp0+Hv748LFy4gODgYEyZMgI+PD3r27ImQkBAMGzYMJ0+eRHBwMKKiouDpqXuhHF0zBtYCCwO5KLCWTyew6s7oFH8v5ETxmqvUEaiQVf9KP8S1JzmijNO8loUo44hB1CZKCQkJmD9/Pm7cuIG6devivffew4gRIwAA586dQ0REBC5fvow6deogODi47G2Xn/4kVlSqIBYG8sHCQF5YGMiIHgqDK+ninFZ1rC2fi+sNqrsiCwP5YGEgHywM5IWFgYywMCgXg+qVoLJ+SeoIpJac4/TinUgv7J14u6KsWLJXQnWiMpyP1qVmUIUBERGRnFTFiw8NqjA4ldxW6gikZmYsr/tuqzWrrlInoCJqFXAGRy6sDOovnHzwx0ZERFROnDEgIiIijYKqVxfor+3yxYsXNR0VLS0t4evri7CwMJiYlD6Cs+0dMeNSBShV1lJHILU66XukjkBFKGwbSh2BNNpIHcAg6aXtckpKCgIDA9GxY0ccP34cP/74I/bt24d169aJdXgiIiK9UwmCKA85EW3GoGjbZTMzM1hZWWH8+PGIiIiAlZUVmjZtiqCgIABA48aNsWbNGs3SyaVlaiTOClNUcVYmqVJHIJInE3OpE5AeVcXbFUWbMXhe2+VDhw7ByckJc+bMQadOndCjRw/ExcXB3t5erMMTERGRCPTSdlmlUmHbtm1wcXHBvn37sGzZMmzevLlYYyUiIiJDwlMJz/G8tssFBQVo06YN/P39AQAtWrTA8OHD8dtvv+H999/XOZ6uJkom8lkxstrLU/HNkAtOXMtMfq7UCaiQ6Yt3qaiqeCpBL22XW7dujWPHjmntr1Kp8Lw2DbraLif+vUmsuERERBUmt0/7YhD1dsX3339fq+3yypUrMWHCBLi5ueG7777DqlWrMHr0aFy9ehUbNmzAmDFjShwrKCgIo0aN0tpmnrZdzLhUAbk2raWOQIVyxWniQkQE6LHtcmJiIr788ktcvnwZFhYWGDp0KMaPH1+mOxOEx9+JFZUqiIWBfJjfOyx1BCpCYd9c6ghUyPStSj/E4fvpoozTsYF8mm8ZVNtlFgbywcJAPlgYyAsLAxnRQ2Hw1z1xCgOvhvIpDAxqSeS/FQOkjkBqtbikhGykWrEFtpy8ZnxB6gikpodrD2UtOzsbgYGBGDx4MAYMKP3fT7bIIyIiKie53q545coVDBs2DGfOnCnzaw1qxqB57ctSRyC1PJWF1BFIrXHuKakjUBGKgrpSR6BCevjoK8fbFY8cOYKpU6di/PjxSE0t+yq1BlUYEBERVXc5OTlISkrS+ZydnR1atGiBP//8E+bm5uVaSJCFARERUTmJdRpA16J+ZmZmMDMzK7ZvYmIiRo4cqXOc5cuXo0ePHhXKUu7CICUlBYMHD0Z4eDg8PDwAPAsbHh6Oq1evwtbWFuPHj0dAQAAAQBAEREVF4aeffkJaWhoaNWqEkJAQvPVW6a8aNU8+Wd64JDKLGrZSRyC1GwO/lDoCFdHkfRepI5CayfDKvytBrMJA16J+EyZMwMSJE4vt6+HhgUuXLolyXF3KVRicPHkSM2fOxK1btzTb0tPT8cEHHyA0NBSDBw9GQkICQkJC4OzsDBcXF6xbtw7btm3DqlWr0KxZM/z555+YNGkSGjZsCBcX/iIREVH1pWtRP12zBfpQ5sJg+/btiIyMRFhYGCZPnqzZvnv3btjY2GDYsGEAgA4dOsDX1xcbN26Ei4sLnjx5gpCQEDRv/uweX29vbzRv3hynTp0qdWEg1Hcua1yqJCnKplJHILUmI1pJHYGKMG7XRuoIpEdiXXxY0mkDKZS5MPDy8oKvry9MTEy0CoMrV67AyUn7fmoHBwds3boVABAaGqr13LVr13DlyhW0asV/1IiIyDAVGM4agaVW5sLAzs5O5/bMzExYWmp33LOwsEBWVlaxfW/cuIGxY8eiX79+aNeuXVkjEBERyYIcb1csau/evWV+jWh3JVhaWuLp06da23JyclCjRg2tbXv37sXMmTMxYMAAzJgxo8TxdF2habkzRqy4VEE2g4KkjkBq97dyfQ85adjyFakjkFrpO/FQUaIVBk5OTjh06JDWtqtXr8LR0VHz9fLlyxETE4N58+bB19f3uePpukLz73meYsUlIiKqMLZdfg4fHx989dVXiI2NxbBhw3Dy5En88ssviIqKAgCsXbsWa9euxcaNG9GyZcsXjqfrCk2jjE1ixaUKylVZvngn0ovar9SSOgIVoWhgL3UE0iMWBs9ha2uLNWvWICIiApGRkahTpw4+/vhjeHp6QhAELF++HNnZ2Zq7FgoFBQVh3LhxxcbTdYWmkCFWWiIiItKlQoXB/y6w0KZNG2zaVPxTvUKhwIkTJypyKCIiItmR+8WH5WFYSyI/LXszCKocpvWzpY5AamnJxe/8IenUuHFT6gikptDDdaBV8VQC2y4TERGRhkHNGGSv3CN1BFIz/7qT1BFI7fguzqTJSd9p5lJHID1SqaROID6DKgyIiIjkRFUFLzIwqMLgxJQfpY5Aaq9mmUodgdR8j70ndQQqyraO1AmIKqTc1xikpKTAx8cHx44d02xLTExEQEAAXF1d4e3tjS1btmieU6lUWLx4Mbp06QI3NzcMGjQIx48fr1h6IiIiCakEQZSHnJSrMDh58iQGDx6ss+1y//79kZCQgIiICMyfPx9nz54FAGzatAm///47tmzZgoSEBPTu3RtBQUHIzc0V5zshIiLSswKVIMpDTvTWdvn69etQqVRQqVQQBAEKhQIWFhZlOrbnT2PKGpcqiSpkttQRSO1E//VSR6Ai3H8fL3UE0iNeY4Dyt10eMmQI/vjjD3Tr1g3GxsYwNzfHt99+C3NzXsFLREQkF3pru5yXl4f27dsjKCgIDRs2xOrVqxEaGoq4uLgSx/xfph1eK2tcqiR3cpxevBPpRZPXbaSOQFRtye36ADGItsCRpaUlcnJytLYVbbs8ffp0dOnSBc2aNYOFhQVCQkJQs2ZN7Nq1S+d4SqUSGRkZWg8iIiI5UakEUR5yore2y/fu3YNSqdQ+uIkJTE113/amq+3yxQ2DxIpLREREOuit7bK3tzdWrFgBd3d32Nvb4/vvv0dycjK6d++uczxdbZcLfvxArLhUQY3tY6WOQGpXbz+VOgIVUe8gG8bJhYk+eiXI7NO+GPTSdhkA5s6di8WLF2PYsGHIzs6Gs7MzVq9ejfr16+scT1fb5XyxwhIREYmgKhYGCkEwnCsnhCtfSR2B1BRNeCGoXOR//73UEagIY1demCsXCte5lX6MbxNuvXinUvig3cuijCMGg1oSmYiISE6q4l0JLAyIiIjKSW6rForBsAoDCyupE5DaY8XrUkcgNetHq6WOQEUYW/HfKTJshlUYEBERyUhVvPiwQoVBSkoKBg8ejPDwcHh4eGi2nz59GiNHjsS5c+d0vu7QoUMYM2YM9uzZg8aNG5f6eMLNfysSl0Rk0/i21BFILTcpU+oIVISQmip1BFJT6OEYVbEwKPfKh7o6LAqCgK1bt2L06NHFFjMqlJycjBkzZkClUpX30ERERLLAtstq27dvx7Rp07SaKAHArFmzsGXLFoSGhup8nUqlwrRp0xAQEFCewxIREVElK9ephJI6LH744Yewt7fHsWPHdL4uKioKdevWxcCBAzUrIpaFssO75YlLlSA5i/dqy0VDz4ZSR6AiFOwYW61UxVMJ5SoMSuqGaG9vX+Jrjh8/jri4OGzbtg1paWnlOSwREZGssDAop5SUFMycOROLFy+GtbV1qQoDpVJZ7DoFqxrssCgXNmbirPZFFSc81X09D0lDuHFT6gikpnCVOoFh0kthcPDgQTx+/Bjvv/8+AGguPOzXrx/GjRuHDz4o3hxJV3fFfy7GVH5YIiKiUiqQ2YWDYtBLYeDn5wc/Pz/N13fu3MGbb76JuLi4Em9X1NVdEThdiSmJiIjKpireYCfbBY50dVcUbp+VKA39r5p2euhnSqWS+yhb6ghUhFFDG6kjEFVIhQuDS5cuFdvm4eGhc3uhxo0bP/d5IiIiQ8CLD6WWkyV1AlIrMK8jdQRSK+DKh7Ji9pqz1BFIj6piYVDulQ+JiIio6jGsGQMiIiIZkdtyxmIwqMLg6de/Sh2B1GqG5kkdgdT+G8n75uXE35fvh1wo9HCNdFU8lWBQhQEREZGcFLAw+H+6Wi7Hx8cjKioKt2/fho2NDQYMGIDg4GAYGT27lGH79u2IiopCcnIymjVrhk8++QSurlyayhAlNSu+KBVJIz9/ndQRqKicHKkTEFVIuS4+1NVy+fz585g+fTomTZqEEydOYNWqVdi2bRtiY2MBAMeOHcPnn3+OBQsWICEhAf369cP48eORnc17sImIyDCpVIIoDzkp84zB9u3bERkZibCwMK3Oinfv3sWQIUPQvXt3AEDz5s3h4+ODhIQEjB49Glu2bEGfPn3g5uYGAAgMDMTmzZvx66+/YuDAgaU6dq1vppY1LlWSi+nsICcXg3/sIHUEKsKoQ1epI5AeVcWLD8s8Y+Dl5YU9e/agd+/eWtt79eqFjz76SPN1Tk4O9u3bh1atWgEArl69Cicn7Va9Dg4OuHjxYnlyExERUSUo84xBSS2Xi8rIyMCHH34ICwsLBAYGAgAyMzNhaWmptZ+FhQWysrhoERERGSa5nQYQg+h3JVy/fh2hoaGoW7cu1q9fD2trawCApaUlcv7nopycnBzY2trqHEdn2+XDu8SOS+XUvovUCahQys5rUkegImxq7pc6AqkZvTW40o9RFQsDUVc+3L9/PwICAtC5c2esXr0atWvX1jzn6OiIK1euaO1/9epVODo66hwrOjoabm5uWg8iIiKqXKLNGJw5cwYhISGYO3cu/P39iz3v7++PkJAQvP3223Bzc8PGjRvx+PFj+Pj46BxPV9vlTPPbYsUlqjJs/FtKHYGKUNR/SeoIpEdVccZAtMJg5cqVyM/PR0REBCIiIjTb3dzcEBMTgw4dOuDTTz/F3LlzkZSUBAcHB6xatQo2NjY6x9PVdvkpF9sjIiIZURWwMNBStHXyypUrX7i/n58f/Pz8KnJIIiIiqkQGtSSyMCFY6gikplgWJXUEUtv6zj6pI1ARAceHSh2B9EhQqaSOIDqDKgyIiIjkhNcYSKzmZ8OkjkBqKSprqSOQmv/2blJHoKLq6L4Fm6qmqlgYiHq7IhEREUnrzp07mDBhAjw9PeHh4YHg4GDcvl36u/pYGBAREZWTHJsohYSEoHbt2ti7dy/27t0LGxsbBAeX/ho9vbZdjo+Px9KlS3Hnzh3Y2dkhKChI55oHJbp9s7xxSWR1axyXOgKppWz9W+oIVIRNvTpSRyA1xSuVfwy53a6Ynp6OevXq4cMPP4SVlRUAYOTIkfDz80N6errWwoMlKVdhcPLkScycOVNn2+UlS5aga9euuHHjBsaOHQsrKyuMHj0aR48excyZM7FkyRJ06dIFx44dw9ixY+Hk5AQXF5fyxCAiIqoSdLUB0LWeD/CsnUBSUpLOcezs7LB69WqtbfHx8WjUqFGpigJAj22XY2NjMXLkSHTt+qwlqaenJ3766Se89FLpVwkrOMc14eXCpI2H1BFILf3mE6kjUBG2DeyljkB6JNZpgOjoaCxbtkxr24QJEzBx4sRi+yYmJmLkyJE6x1m+fDl69Oih+fqHH37AmjVrsGLFilJnKXNh4OXlBV9fX5iYmGgVBr169UKvXr00Xxe2Xfb19QUAnD17Fh4eHvjggw+QmJgIe3t7TJw4sVgrZiIiIkMhiFQY6GoDoGu2AAA8PDy0FhjURalUYv78+fj1118RHR0NT0/PUmfRW9vl9PR0rF69GkuXLkWbNm2wd+9eTJ48GRs2bMDrr79e1hhERERVRkmnDcojJSUF48ePh1KpxNatW9GkSZMyvV5vbZfNzMwwcOBAuLq6AgB69uyJDh06ID4+XmdhoOt8Sw2/t8WOS+X01Li51BFI7ZXZXaWOQFRtqWS28mFeXh7GjBkDW1tbLF++HBYWFmUeQ9TCYP/+/ZgyZQoGDRqEqVOnwsTk/4dv3rx5sT/0BQUFEATd0zC6zrdcPPyxmHGJiIgqRG4LHP3555+4cOECzM3N0aFDB63ndu7ciYYNG75wDL21XR46dCg+//xzdO7cGZ6entizZw+OHTuGKVOm6BxP1/kWhRAvVlyqICuTVKkjUKGcXKkTEJFM9OzZ84XXH7yI3touDxw4EEZGRpg/fz7u3LmDRo0aYfHixWjVqpXO8XSeb3kqVloiIqKKk9s6BmLQa9vld955B++8805FDklERCQbcjuVIAaDaqIkpD2QOgKpZVm0lDoCFdp5ReoEVEQNrnwoG3pZ+bAKFgbslUBEREQaBjVjULDnkNQRSM1qlKvUEUgtOTlL6ghUhHVzZ6kjkB6JtcCRnBhUYUBERCQnPJVAREREVZqobZc3btyIdevWITk5GXZ2dhg5ciSGDx8OABAEAVFRUfjpp5+QlpaGRo0aISQkBG+99Vapj1mQxClTuVDm20odgdSe3uZ9vHJSP+Wh1BGo0ItX8K8w3q6opqvt8t69e/HNN99gzZo1aN26Nc6ePYvhw4fDwcEBnp6eWLduHbZt24ZVq1ahWbNm+PPPPzFp0iQ0bNiQbZeJiMggyW1JZDGI1nbZ29sbe/fuhbW1NfLz85GamgqFQoFatWoBAJ48eYKQkBA0b95cs3/z5s1x6tSpUhcGqSd5u6Jc1L+8XeoIpPbgXoHUEagIhyzObJJhE63tMgBYW1vj+vXr6Nu3LwoKCjBq1Ci0bPnsfvfQ0FCtfa9du4YrV66UuPIhERGR3FXFiw9Fb7vcpEkTJCYm4uLFiwgODkadOnXwwQcfaO1z48YNjB07Fv369UO7du3KGoGIiEgWWBiUgqmpKQCgTZs2GDlyJH755RetwmDv3r2YOXMmBgwYgBkzZpQ4jq62y/UXjxA7LpVThr231BFIrW3f36WOQEUI6U+kjkBqCqkDGCjRCoPY2FicOXMGS5Ys0WxTKpWoXbu25uvly5cjJiYG8+bNg6+v73PH09l2+ffQEvYmIiLSP84YPIe7uzu+/vpr/Prrr3jrrbdw+vRprF+/Hp9++ikAYO3atVi7di02btyoue7geXS1XUbGJrHiElUZlu3spY5ARRi5ekgdgfRI4O2KJWvdujUiIyOxZMkSfPzxx2jUqBFmz56N3r17QxAELF++HNnZ2Rg2bJjW64KCgjBu3Lhi4+lquyxkiJWWiIio4jhj8D+Ktl0Gnt2C6O1d/NyzQqHAiRMnKnKoZ+PU4KI6cpGZr4eVQ6h0Engbr5zUHGIudQSiCmGvBCIionLijAERERFpCFz5UFpPpi178U6kF3YrG0gdgdSun0qSOgIVUePAbqkjkJrRW/2ljmCQDKowICIikhPelSCxmp8Ne/FOpB+pN6ROQGr2b9SXOgIVlZUtdQLSI6EKXmNgVN4XpqSkwMfHB8eOHdNs27hxI3r27AlXV1f07NkTGzZs0DynUqmwePFidOnSBW5ubhg0aBCOHz9esfREREQkKr21Xd60aRN+//13bNmyBXZ2dli/fj2CgoJw9OhRmJvz9h4iIjI8PJWA8rddvn79OlQqFVQqFQRBgEKhgIWFRdkOnpdb1rhUSRQvvSp1BFIztjKoM4JVnsKtrdQRSI+q4qkEvbVdHjJkCP744w9069YNxsbGMDc3x7fffsvZAiIiIhnRW9vlvLw8tG/fHkFBQWjYsCFWr16N0NBQxMXFvXDMQgq7V8oalypJgcJS6gikZvF2C6kjEFVfBVVvHYNyX3xYElNTU5iammraLv/3v/8FAEyfPh1dunRBs2bNYGFhgZCQENSsWRO7du3SOY5SqURGRobWg4iISE4ElSDKQ0701nb53r17UCqV2gc3MYGpqanO8XS1Xb6UuEisuERERBXGiw+f40Vtl729vbFixQq4u7vD3t4e33//PZKTk9G9e3ed4+lqu6w6MFOsuFRBxj3ekToCqWXvvyZ1BCrC3LqG1BFITcGzz+Wil7bLADB37lwsXrwYw4YNQ3Z2NpydnbF69WrUr697cRZdbZer3pkcIiIyZHI7DSAGhSAIBvNdCQmfSB2B1BRu3aSOQGpPQyKkjkBF1PDhx1S5MBqwttKP0fW9zaKMs3/dYFHGEYPoFx8SERGR4eLKKEREROXEiw8lJqSmSh2B1BRSByANy3b2Ukegoqy4xkd1UhWvMeCpBCIiItIo94xBSkoKBg8ejPDwcHh4eGg99/DhQ/Tv3x/Tpk3DgAEDir320KFDGDNmDPbs2YPGjRuX/qA+8rk4o7p7rGwqdQRSqy11ANKieLWp1BFIj6riqYRyzRicPHkSgwcP1uquWEilUmHatGlILWHaPzk5GTNmzIBKxZsPiYjIsFXFlQ/LXBhs374d06ZNK9ZAqdDy5cthb2+PBg0aFHuusGgICAgoe1IiIiKqdKJ2Vzx69Ch27tyJn376Cb6+vsVeGxUVhbp162LgwIGIiooqe9pDcWV/DVWKuu5dpY5Aane2XpY6AhXRsKGN1BFITeGsh4NUwSZKonVXfPz4MWbNmoXIyEjUqFF8SdDjx48jLi4O27ZtQ1paWpmDEhERyY3cTgOIQZTbFQVBwPTp0zFixAi0bt262PMpKSmYOXMmFi9eDGtr61IVBkqlsljTpRrmFmLEJTHk5UqdgNSsXuLtcXKievRU6gikpo/b7qrixYeiFAb379/H8ePHkZiYiOXLlwMAMjIy8NlnnyE+Ph69e/fG48eP8f777wOA5sLDfv36Ydy4cfjggw+Kjamru+LFDYPEiEtEREQlEKUwaNiwIc6dO6e1zdvbGxMmTNDcrujn56d57s6dO3jzzTcRFxdX4u2Kuror4p+FYsQlIiISBU8l6JGu7opV78dvuAqsi991QtKwdud7ISdG9WpKHYH0iKcS/selS5dKfG7v3r0lPte4cePnvpaIiIikIdsZA52asJ2pXNzLel3qCKTWsL6V1BGoCK58WM1UwcX6DKswICIikhGeSpDaU3ZXlIuG9ROljkBqBUlZUkegIoyy+H6QYTOswoCIiEhGeFcCERERafBUgtTq2EudgNSMUm9IHYHUlEmZUkegIkySHkodgdQUUgeQyD///IP58+fjwoULMDExQZcuXTBr1izY2tqW6vX6WDGSiIioalKpxHmIRKlUYuzYsfDw8MCxY8ewZ88eJCcnY8GCBaUew6BmDBQ2nDGQiwKj4o2ySBqmr9aWOgIVoXhNHy39SC7kdirBzMwMu3fvhoWFBYyMjJCeno7s7GzUqVOn1GMYVGFAREQkJ1JcfJiTk4OkpCSdz9nZ2cHK6tnaJkOGDMHp06fh4OCg6VVUGiwMiIiIJKaro7Cu1gAAkJiYiJEjR+ocZ/ny5ejRowcAIDY2Frm5uZg7dy5GjRqFHTt2wNjY+IVZFIIgyGsepIpTKpWIjo5GUFCQzjec9IfvhXzwvZAPvhfSWLp0abGOwhMmTMDEiRMrPPbjx4/RsWNHbN++HS1btnzh/iwM9CwjIwNubm44efIkrK2tpY5TrfG9kA++F/LB90IaZZkxeJ47d+5g5MiR2LRpE1566SUAwP3799GtWzfs3bsXjRo1euEYvCuBiIhIYmZmZrC2ttZ6lGfGplGjRrCxscH8+fORmZmJlJQUfPbZZ+jSpUupigKAhQEREVGVoVAoEBUVhfz8fHh7e8PPzw8NGjTAf/7zn1KPwYsPiYiIqhB7e3ssXbq03K/njIGemZmZYcKECbyoRwb4XsgH3wv54HtBvPiQiIiINDhjQERERBosDIiIiEiDhYGBevjwIbKysqSOUa3dvHlT6giVoqCgALdv35Y6RpkYYuaykvv3+O+//0odgURicIVBeno65s6di65du6Jt27bw8vLCjBkz8ODBA70cf8SIESVe7fm858T06NEj9OrVCykpKQCerZg1YsSISj1mdnY2Bg8ejG3btul8Xs7vS2mNGTMGK1euLPF5Z2dnHDt2DACwcOFCrFixQudzYvvhhx/Qq1cvuLq6olevXti4cWOJ+3p7e6NNmzZwdXWFq6ur5r1YuHAhVKXs4DZ58mTs2LGjVPtu27YN3t7eZX5ObEUz37lzB87Ozrhz547ox8nNzcXnn3+OTp06wdXVFYMGDcKRI0de+Do5vS+lFRcXhz59+pT4/MyZMzFz5kwAwN9//42+ffvqfK6yFBQUYMSIEZV+nOrI4AqDyZMnIzU1FVu3bsWZM2ewY8cOKJVKjBo1Cvn5+VLH04ucnBy9zhZcuXIFw4YNw5kzZ0rcpyq8LzExMRg3blyp9k1NTa3kNM/8/vvv+M9//oOFCxfi1KlTWLBgAZYsWYL4+PgSX/PZZ5/h9OnTOH36NM6cOYPVq1djx44dxZZbLYm+vjcx6Svz4sWLkZiYiB07duDkyZPw8/NDcHAwMjMzX/haQ3tf+vXrh507d5Zq36dPnyIvL6+SE2lbtmwZTpw4oddjVhcGVxicPHkSPj4+sLOzAwDUq1cPs2bNwuuvv44nT54AeLak57x589C1a1d06NABkydPxqNHjwD8/6eJ7777Dp06dYKbmxvCwsKQkZEB4NmylAsXLsTbb78NV1dXdOjQAZ9//jnKevOGIAhYv349evXqBXd3d7z77rs4f/685nlvb29ER0ejf//+cHV1Rf/+/XH06FHN83///TeGDh0KV1dX+Pn5YcWKFfD29kZBQYGmMu/bty9+/fVXAEBmZiY+/vhjeHl5wcPDA4sXLy71z7NVq1bYv38/AODBgwfw8PDApk2bAABHjhzBe++9h3feeQcNGzZ87jhyfF82bNgAPz8/zdfbtm2Ds7Mzrl27BgB48uQJWrdujdu3b2vNOuTl5WH+/Pnw8PCAp6cnYmJiNGMsX74cv/zyC3755Rf069dPs/3QoUPw8/ODq6sr/P39cfny5Rf+/AVBwNixYzFkyBAUFBQAeDYb0atXL2RkZCApKQljx45F27ZtoVAo4OrqCg8PDyQkJLxw7ELOzs5o164d/v77bwDPfpbffPMN3nzzTbRv3x5jx47VnBaZPXs2Tpw4gejoaE2RtHfvXgwZMgQdOnTA66+/juHDh5dr2vjChQsYMWIE2rVrh549eyI2Nlbz/i1duhShoaGYNm0a3N3d0aVLFyxatEjz2pycHHz66ado3749unbtiiVLlsDb2xvHjh3TmRkAfvnlF7z99tto27YtAgMDS+xGV5RSqYSfnx8mTZqk2fbhhx/i3XffRX5+PsLCwvDdd9/Bzs4OOTk5SEtLQ82aNWFqalrmn4cU70t6ejpatWqFf/75B8CzGRAXFxd89dVXmn1CQ0PxzTffFJt1+OOPP9CnTx+0bdsWQUFBmkLl9u3bGDt2LADA1dUVp0+fBvBsff7Q0FB4eHjAy8sLGzZsKNXPZefOnWjdujUuXrwI4Nm/hS4uLjhw4IBmnyNHjmD37t3o2bNnqcakMhIMzEcffSS88cYbwqeffirs3LlTuHPnTrF9Jk6cKIwePVp49OiRkJGRIXz88cfC4MGDBZVKJdy+fVtwcnIShg8fLjx+/Fh4+PChEBAQIEybNk0QBEH49ttvhT59+ghJSUmCIAjCqVOnhJYtWwqHDx8WBEEQhg8fLkRGRurMVvS5DRs2CN26dRP++ecfQalUClu2bBHc3d2F5ORkQRAEoXv37oKPj4/w77//CllZWcKMGTOEXr16CYIgCE+fPhU6dOggLFmyRMjNzRUuXrwodOvWTejevbsgCILme7h9+7YgCIIQGRkpODs7Czt27BBUKpVw5MgRwdnZWTh16lSpfqZLly4VvLy8hMePHwtDhw4VpkyZonkuJSVFyMnJ0WT+6aefDOp9uX//vuDs7Cw8ePBAEARBmDx5suDi4iKsW7dOEARBiIuLE/r161dsjCVLlgg9e/YUbt26JWRmZgphYWGCk5OTcPToUUEQBGHGjBnCjBkzNMdxcnISBg8eLCQnJwvZ2dnCmDFjhNGjR5fq5//o0SOhU6dOwrfffiscOHBAeP3114V//vmnxH3bt28vbN++Xefz//seKZVK4ejRo0K7du2E9evXC4IgCAsWLBD69+8v3Lp1S8jJyRGWLl0qeHt7a97noj+H+/fvC61btxb++OMPQRCe/f/w7rvvat6Xn376SfP/5f8q+tyDBw8ENzc3YcOGDYJSqRSuXLki+Pj4CD/88IMgCP////D27duF/Px8Yd++fYKzs7Nw+vRpQRAE4ZNPPhHeeecd4d69e0JGRkax96No5sL/l0JCQoQnT54IaWlpQv/+/YVPPvnkxW+GIAhXr14VXn/9dWHnzp3Cpk2bBA8PD83/P4U2bdokODs7C61atRJ+++23F44pp/clMDBQWLlypSAIgnDgwAHBxcVF6N+/vyAIgpCbmyu4uroKf//9t9YY165dE1q1aiX8/PPPQl5enrBnzx7htdde0/wOHD16VHByctIcY8aMGULr1q2FQ4cOCSqVSti2bZvW7+GLzJw5U/D19RXS0tKEnj17CosWLdI89+jRI6F79+7CP//8U+z3kMRhcDMG4eHhmDNnDu7fv485c+bA29sbPj4+iIuLA/CsSo2Pj8fs2bNRt25d1KhRA7NmzcK5c+dw4cIFzTgfffQR6tSpAzs7O4SGhmLXrl1QKpUYNGgQYmNjYWdnh4cPHyInJwc1atQo1aeNojZu3IigoCC0aNECpqam8Pf3R/PmzTU5AcDf3x+vvPIKLC0t4evrq6n29+7dC2NjY0ycOBFmZmZwdnbGmDFjnns8R0dH+Pn5QaFQwNPTE/Xq1cOtW7dKlTU4OBhNmzaFv78/Hj9+jHnz5mmes7W1hbm5+QvHkOv7Ym9vj1atWuHgwYNQqVQ4fPgwhgwZgsOHDwN49rP28fEp9rqff/4Z77//Ppo0aQIrKyt8/PHHUCgUzz3WqFGjUK9ePVhYWKBHjx6l/vnXrVsXCxcuxPLlyzFjxgzMmjULLVq0KLZfcnIyxo4di9atW2udz/1fn332Gdzd3eHu7q6ZWRk1ahSGDx8OQRCwadMmTJkyBU2aNIG5uTlCQkKQl5eHffv2FRurTp062LlzJ7y9vZGRkYEHDx7A1ta2zL8PcXFxaN68OYYNGwZTU1NNf/ii10s0bdoU/fv3h7GxMbp27Qo7Ozv8+++/yMvLQ1xcHCZPnowGDRqgRo0amDNnzgvbx44bNw41a9ZE7dq10blz51K/H82bN8fs2bMxb948LFiwAF999RXq16+vtU///v1x7tw5LFy4ENOmTcPJkydfOK5c3pcePXpoPn3/9ddfGDx4MC5duoSUlBQcPXoUtra2eO2117Re8+uvv6J169bo168fTExM0KNHD3Tv3v25x+nUqRM6duwIhUKBPn36QBCEUl88+cknn0CpVOKdd96BnZ0dPvzwQwCASqVCWFgYRo0apfN3hMRhcEsiGxkZwc/PD35+fhAEAdeuXcPPP/+M6dOnw87ODjVq1AAADBo0SOt1xsbGuHPnDmxsbAAAr7zyiua5Bg0aQKlUIi0tDSqVCvPmzUNCQgLs7e3RsmVLCIJQ6guECt29excLFy7E119/rdmWn5+P1q1ba76uV6+e5r9NTEw006oPHjxAw4YNYWT0/3VbkyZNnnu8wu+rkJmZmWZq+kWMjIwwdOhQTJ48GSEhIZqfYVnI+X3x8fHBgQMH4OTkBBsbG7zzzjsYNmwYcnJycODAAQQHBxd7zcOHD9GgQQPN17Vq1ULt2rWfe5yi74GpqWmpf/4A0LFjRzRp0gT37t3DW2+9Vez5M2fO4MMPP4S7uzvmz58PE5OSf3U//fRTDBgwQOdzjx8/RlZWFj788EOt/7/y8vJw9+7dYvubmpriv//9LzZt2gSFQgEnJydkZGQ89/i63L17FxcuXIC7u7tmm0ql0vrjXngaquixVSoV0tLSkJ2drdUAxtraGra2ts89ZkXeD19fX3z99deoV68ePD09iz1fWCz36dMHO3bswG+//QY3N7fnjimX96VHjx6YP38+nj59ioMHD+KLL77A8ePHcfToURw7dkzn9HxSUlKxU4kvv/zyc697KPrzL1xFsbTvgZWVFQYOHIivv/4aISEhmv9PoqOjYWZmVukXW1d3BlUYHDx4EKGhofjzzz9hY2MDhUIBBwcHTJ06FYcOHdK6Mva3337T+ofm6tWraNKkCZKTkwE8+x+9WbNmAJ6d37a0tIStrS3Gjx+P2rVr46+//oK5uTlUKhXatWtX5qz29vYIDQ3Vuqr31q1bxf6A69KwYUPcu3cPgiBoPqXeu3evzBlKKy0tDQsXLsTAgQMRExMDHx+fYp8Ynkfu70uPHj0QExMDJycneHl5oUWLFrC0tERMTAzq1asHR0fHYq+xt7fX+nSTlZWFp0+flvpnUlarVq1CdnY2WrdujTlz5mDJkiWa57Zu3Yrw8HCEhoZi9OjRFTpO4QzQmjVr0LZtW83269evF/tUDDx7vzZs2IAffvhBU7R9/vnnpbp+oih7e3t4eHhg9erVmm2pqamlumivbt26sLCwwL179zT/b2RlZVXqxXjz58/Hq6++ioyMDCxZsgRhYWEAgEmTJmmuWSikVCpL9Xv9PPp8X+rXr48WLVpg27ZtePToEdq0aQMvLy8cPnwYBw8e1Pp/r5C9vX2xmYsHDx6UajaxPG7duoUVK1YgICAAX375JTp16gR7e3v8/PPPePjwoabAzMnJAfDsIl1eiCgegzqV0K5dO9StWxcfffQRLl26hLy8PGRkZCAuLg7//vsvunXrhvr166Nbt26IiIhAamoq8vLysGLFCvj7+2suggOARYsWaS7uioyMhJ+fH0xNTZGRkQFzc3MYGRkhIyMDX375JTIyMsp8xe2gQYOwYsUKzUVuBw8eRJ8+fUp10Zi3tzcEQcDKlSuhVCpx/fp1rX9QC38ZCy/Mq6iPP/4YDg4O+OKLLzB06FBMmTIF2dnZpX693N8XBwcH1K1bFxs2bECnTp0APPuEHhMTU+LFSwEBAYiJicG1a9eQm5uLBQsWaH3aMTMzE61QOHfuHJYuXYoFCxZgwYIF+Ouvv7B161YAQHx8PObOnYulS5dWuCgAns3s+Pv7Y9GiRXjw4AFUKhW2b9+Ovn37ai50K/q9PX36FEZGRrCwsIAgCDhw4AB27NhR5t8HX19fnDlzBnFxccjPz8fDhw8xbtw4LFiwoNSZly5diqSkJGRnZ2P+/PmV9n78/vvviIuL07wf69at05x6cnV1xapVq3Dp0iXk5+djy5YtOHfunNZFqOWh7/fFx8cHK1asgKenJ4yNjdGpUyf897//hUql0ipMCvXr1w+XL1/Gjz/+iPz8fPz111/Ys2eP5vnCf5PEeA/y8vIwZcoU9OnTB+Hh4WjXrh3CwsKgUqmwa9cunDp1CidOnMCJEyfQt29f9O3bl0WByAyqMLCwsMD3338POzs7jB8/Hu7u7ujWrRvi4uKwdu1aNG/eHADw5ZdfolatWujfvz88PT2xf/9+xMTEaH1Sffnll9G3b1/069cPrq6umDVrFoBnfyQvXryI9u3b46233kJGRgY6d+5c5k9IgYGB6N+/P4KDg+Hq6oqIiAjMmTMHb7755gtfa2VlhaioKPzxxx9o3749pkyZgk6dOmmufK5Xrx58fHwwePBg/PDDDy8cLy4uDq6urjqf++GHH3Ds2DFEREQAAKZMmQKFQqH5ujQM4X3x8fFBRkYG2rdvDwDw8vJCdna2zusLAGDs2LHo168fhg8fDi8vL9SsWVPrU2Hv3r1x6tQpdOvWrVTH79Onj841EjIzMzF16lQMHz4c7u7uaNCgAWbPno2IiAjcuHEDy5YtQ0FBAUJDQzX3wLu6umLOnDmlOq4uM2bMwOuvv453330X7u7uiI2NRWRkJFq2bAng2fnzn376Ce+++y7eeecddOzYEX369IGnpydWrFiB9957Dzdu3IBSqSz1MRs1aoSYmBhs3rwZHTt2hJ+fH5o1a1aqwgAApk6dimbNmqF3797o1asX7O3tYWRkpPmdKJq5NFxdXbWu9ymUlJSE2bNnY9q0aWjatClat26NcePGYfr06UhJScHIkSPx3nvvYfz48ejQoQPi4uIQGxuLl19+udQ/i5Lo833p0aMHUlNTNYWym5sbFAoFevToofNamiZNmmDlypXYuHEj3NzcEBUVpfW74+TkBDc3N3Tu3Flzh9PzrFy5ssQ1Er755hukpqZq1ieYN28erl69iujo6BeOS+Kodk2U7ty5gzfffBN//PEHGjduLHUcnVJTU3H9+nWtc5bfffcddu7cqbmNsKwCAwMRGxsrUkLxGcL7UhEHDx7EpUuXXngRKemWkJAAZ2dn1KpVC8Cz2TI3NzfEx8ejadOmZR5v06ZNqF27Nt5++22Rk1JpCIKA0aNHY+3atVJHIR0MasaguigoKMB7772nqbzv3LmD77///oVXAZfk9OnTpf5kS5XjwIED8PX1lTqGwVqzZg0iIiKQk5OD3NxcREZG4tVXXy1XUSAIAs6dO4cuXbqIH5RKZc+ePfD395c6BpWAMwYy9fvvv+Obb77BnTt3UKtWLbzzzjuYMGFCma8GNxSG8r6QNJKSkvDZZ5/h5MmTKCgogJubG2bPni3KFD4Raat2hQERERGVjKcSiIiISIOFAREREWmwMCAiIiINFgZERESkwcKAiIiINFgYEBERkQYLAyIiItJgYUBEREQaLAyIiIhI4/8AHj8jiCGnk5YAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax = sns.heatmap(X_demean,  # 绘制去均值矩阵的热力图\n",
    "                 cmap='RdYlBu_r',\n",
    "                 xticklabels=list(X_df.columns),\n",
    "                 cbar_kws={\"orientation\": \"vertical\"},\n",
    "                 vmin=-3, vmax=3)\n",
    "plt.title('$X_{demean}$')  # 设置标题"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24f4dda4-94b0-4a39-a457-34dbc92aab06",
   "metadata": {},
   "source": [
    "## 计算去均值矩阵的平方和"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d75ad737-ae90-4491-b44c-4eaf249b0bf8",
   "metadata": {},
   "outputs": [],
   "source": [
    "SSD = (np.linalg.norm(X - E_X, axis=1) ** 2).sum()  # 计算去均值矩阵的平方和"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bca89c3f-ceb4-4132-9b3e-3ee2c1e85738",
   "metadata": {},
   "source": [
    "## 去均值特征分布的核密度估计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d7b8ed73-af6a-4cbc-bbf0-ae23d15987de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Distribution of $X_{demean}$ columns')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "sns.kdeplot(data=X_demean, fill=True, \n",
    "            common_norm=False, \n",
    "            alpha=.3, linewidth=1,\n",
    "            palette=\"viridis\")  # 绘制去均值特征分布的核密度估计图\n",
    "plt.title('Distribution of $X_{demean}$ columns')  # 设置标题"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d28161c-016b-4c73-bf9c-6003e063b9d7",
   "metadata": {},
   "source": [
    "## 计算协方差矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7079b74f-9b24-4dbd-91c9-31e54ddc3aa5",
   "metadata": {},
   "outputs": [],
   "source": [
    "SIGMA = X_df.cov()  # 计算 X 的协方差矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1fdf6de8-6407-4bd3-ba08-fcc8aafb5abc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$\\\\Sigma$')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots()\n",
    "h = sns.heatmap(SIGMA, cmap='RdBu_r', linewidths=.05, annot=True)  # 绘制协方差矩阵的热力图\n",
    "h.set_aspect(\"equal\")\n",
    "h.set_title(r'$\\Sigma$')  # 设置标题"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6eb5f9c-d2fb-469b-8e61-2538440a91cc",
   "metadata": {},
   "source": [
    "## 计算线性相关矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fce7ac21-5923-47d3-9c95-8f76295a1348",
   "metadata": {},
   "outputs": [],
   "source": [
    "RHO = X_df.corr()  # 计算 X 的相关矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "abcc0c5f-bddf-4cfc-bb30-748538b771cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$Ρ$')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots()\n",
    "h = sns.heatmap(RHO, cmap='RdBu_r', linewidths=.05, annot=True)  # 绘制相关矩阵的热力图\n",
    "h.set_aspect(\"equal\")\n",
    "h.set_title('$\\u03A1$')  # 设置标题"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb30b8ac-b19b-42a8-ae71-5e183373ec51",
   "metadata": {},
   "source": [
    "## 比较各类的协方差矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "742a1534-543a-4605-bc70-7b577a13d5cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Y = 2, virginica')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True)\n",
    "\n",
    "g1 = sns.heatmap(X_df[y == 0].cov(), cmap=\"RdYlBu_r\",  # 绘制类别 0 的协方差矩阵\n",
    "                 annot=True, cbar=False, ax=ax1, square=True,\n",
    "                 vmax=0.4, vmin=0)\n",
    "ax1.set_title('Y = 0, setosa')  # 设置标题\n",
    "\n",
    "g2 = sns.heatmap(X_df[y == 1].cov(), cmap=\"RdYlBu_r\",  # 绘制类别 1 的协方差矩阵\n",
    "                 annot=True, cbar=False, ax=ax2, square=True,\n",
    "                 vmax=0.4, vmin=0)\n",
    "ax2.set_title('Y = 1, versicolor')  # 设置标题\n",
    "\n",
    "g3 = sns.heatmap(X_df[y == 2].cov(), cmap=\"RdYlBu_r\",  # 绘制类别 2 的协方差矩阵\n",
    "                 annot=True, cbar=False, ax=ax3, square=True,\n",
    "                 vmax=0.4, vmin=0)\n",
    "ax3.set_title('Y = 2, virginica')  # 设置标题"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7a8dc5a-d964-419e-befd-595558dd36f9",
   "metadata": {},
   "source": [
    "## 比较各类的相关矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8fd78370-fd4b-4974-a4fe-a7871ca97d5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Y = 2, virginica')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True)\n",
    "\n",
    "g1 = sns.heatmap(X_df[y == 0].corr(), cmap=\"RdYlBu_r\",  # 绘制类别 0 的相关矩阵\n",
    "                 annot=True, cbar=False, ax=ax1, square=True,\n",
    "                 vmax=1, vmin=0.15)\n",
    "ax1.set_title('Y = 0, setosa')  # 设置标题\n",
    "\n",
    "g2 = sns.heatmap(X_df[y == 1].corr(), cmap=\"RdYlBu_r\",  # 绘制类别 1 的相关矩阵\n",
    "                 annot=True, cbar=False, ax=ax2, square=True,\n",
    "                 vmax=1, vmin=0.15)\n",
    "ax2.set_title('Y = 1, versicolor')  # 设置标题\n",
    "\n",
    "g3 = sns.heatmap(X_df[y == 2].corr(), cmap=\"RdYlBu_r\",  # 绘制类别 2 的相关矩阵\n",
    "                 annot=True, cbar=False, ax=ax3, square=True,\n",
    "                 vmax=1, vmin=0.15)\n",
    "ax3.set_title('Y = 2, virginica')  # 设置标题"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "443c36be-605f-4f93-81a2-9405339e8d0c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
